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BEGIN:VEVENT
SUMMARY:Group solvency tests\, intragroup transfers and intragroup diversi
fication: a set-valued perspective
DTSTART;VALUE=DATE-TIME:20150903T085000Z
DTEND;VALUE=DATE-TIME:20150903T092000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2369@indico.math.cnrs.fr
DESCRIPTION:Speakers: Michael Schmutz (University of Berne)\nThe aim of ri
sk-based solvency frameworks\, such as Solvency II to be introduced in the
EU and the Swiss Solvency Test (SST) that has been in force in Switzerlan
d since 2011\, is to assess the financial health of insurance companies. T
his is achieved by quantifying capital adequacy by calculating the solvenc
y capital requirement (SCR). These calculations are based on scalar risk m
easures. Assessing the financial health of insurance groups (of several co
nnected companies) is an even more challenging task\; a variety of approac
hes can be taken to tackle the issue. Aspects of the most well-known appro
aches\, and modified versions of them\, are discussed based on a set-value
d perspective.\n\nhttps://indico.math.cnrs.fr/event/699/contributions/2369
/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2369/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robust Detection of Unobservable Disorder in Poisson rate
DTSTART;VALUE=DATE-TIME:20150904T070000Z
DTEND;VALUE=DATE-TIME:20150904T074000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2370@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nicole El Karoui (UPMC)\nWe consider the non-Bayesia
n quickest detection problem of an unobservable time\nof change in the rat
e of an inhomogeneous Poisson process. We seek a stopping\nrule that minim
izes the robust Lorden criterion. The latter is formulated in terms\nof th
e number of events until detection\, both for the worst-case delay and the
false\nalarm constraint. In the Wiener case\, such a problem was solved u
sing the so-\ncalled cumulative sums (cusum) strategy by many authors (Mou
stakides (2004)\,\nor Shyraiev (1963\,..2009)). In our setting\, we derive
the exact optimality of the\ncusum stopping rule by using finite variatio
n calculus and elementary martingale\nproperties to characterize the perfo
rmance functions of the cusum stopping rule in\nterms of scale function. T
hese are solutions of some delayed differential equations\nthat we solve e
lementary. The case of detecting a decrease in the intensity is easy to\ns
tudy because the performance functions are continuous. In case of increase
where\nthe performance functions are not continuous\, martingale properti
es require using a\ndiscontinuous local time. Nevertheless\, from an ident
ity relating the scale functions\,\nthe optimality of the cusum rule still
holds. Numerical applications are provided.\nThis is joint work with S.Lo
isel (ISFA) and Y.Sahli (ISFA).\n\nhttps://indico.math.cnrs.fr/event/699/c
ontributions/2370/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2370/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Incomplete stochastic equilibria and a system of quadratic BSDEs
DTSTART;VALUE=DATE-TIME:20150904T095000Z
DTEND;VALUE=DATE-TIME:20150904T102000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2371@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hao Xing (London School of Economics)\nWe tackle a n
umber of problems related to the existence of continuous-time stochastic R
adner equilibria with incomplete markets. Various assumptions of "smallnes
s" type-including a new notion of "closeness to Pareto optimality"-are sho
wn to be sufficient for existence and uniqueness. Central role in our anal
ysis is played by a fully-coupled nonlinear system of quadratic BSDEs.\n\n
This is a joint work with Kostas Kardaras and Gordan Zitkovic.\n\nhttps://
indico.math.cnrs.fr/event/699/contributions/2371/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2371/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the supremum of fractional Brownian motion and related processe
s
DTSTART;VALUE=DATE-TIME:20150902T162000Z
DTEND;VALUE=DATE-TIME:20150902T165000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2372@indico.math.cnrs.fr
DESCRIPTION:Speakers: Mikhail Zhitlukhin (Steklov Mathematical institute)\
nThis paper studies the expected value of the supremum of fractional Brown
ian motion and related Gaussian processes. We obtain upper and lower bound
s for the expected supremum and bounds for the approximation of the suprem
um of a continuous process by random walks. As corollaries\, we obtain res
ults on the structure of fractional Brownian motion when the Hurst paramet
er H tends to zero.\nThis is a joint work with Konstantin Borovkov\, Yulia
Mishura and Alexander Novikov.\n\nhttps://indico.math.cnrs.fr/event/699/c
ontributions/2372/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2372/
END:VEVENT
BEGIN:VEVENT
SUMMARY:An Analytical Approximation for Pricing VWAP Options
DTSTART;VALUE=DATE-TIME:20150904T075000Z
DTEND;VALUE=DATE-TIME:20150904T083000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2373@indico.math.cnrs.fr
DESCRIPTION:Speakers: Masaaki Kijima (Tokyo Metropolitan University)\nThis
paper proposes a unified approximation method for various options whose p
ayoffs depend on the volume weighted average price (VWAP). Despite their p
opularity in practice\, quite few pricing models have been developed in th
e literature. Also\, in previous works\, the underlying asset process has
been restricted to a geometric Brownian motion. In contrast\, our method i
s applicable to the general class of continuous Markov processes such as l
ocal volatility models\, stochastic volatility models\, and their combinat
ions. Moreover\, our method can be used for any type of VWAP options with
fixed-strike\, floating-strike\, continuously sampled\, discretely sampled
\, forward-start\, and in-progress transactions. (joint work with H. Funah
ashi)\n\nhttps://indico.math.cnrs.fr/event/699/contributions/2373/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2373/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debt negotiation with firms’ cross-holdings of securities
DTSTART;VALUE=DATE-TIME:20150902T151000Z
DTEND;VALUE=DATE-TIME:20150902T154000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2374@indico.math.cnrs.fr
DESCRIPTION:Speakers: Teruyoshi Suzuki (Hokkaido University)\nWe analyze t
he interaction of the debt renegotiation between two firms that cross-hold
their issuing debts and equities. When the firms are reciprocally the maj
or shareholder and/or debt holder of the other firms\, the possibility of
debt renegotiation will affect each other. We first develop models of debt
renegotiation scheme: debt equity swap and strategic debt service with ga
me-theoretic setting under continuous time models. We then derive the opti
mal boundaries in each model to offer debt renegotiation by equity holders
of the one firm to those of the other firm. We show that the simultaneous
debt renegotiation can happen when firms cross-hold their debts and we pr
esent the comparative statics of the renegotiation boundaries.\n\nhttps://
indico.math.cnrs.fr/event/699/contributions/2374/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2374/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Universal Arbitrage Aggregator in Discrete Time under Uncertainty\
,
DTSTART;VALUE=DATE-TIME:20150901T070000Z
DTEND;VALUE=DATE-TIME:20150901T074000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2375@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marco Frittelli (Università degli Studi di Milano)\
nIn a model independent discrete time financial market\, we discuss the ri
chness of the family of martingale measures in relation to different notio
ns of Arbitrage\, generated by a class S of significant sets\, which we ca
ll Arbitrage de la classe S. The choice of S reflects into the intrinsic p
roperties of the class of polar sets of martingale measures. In particular
: for S = {Ω}\, absence of Model Independent Arbitrage is equivalent to t
he existence of a martingale measure\; for S being the open sets\, absence
of Open Arbitrage is equivalent to the existence of full support martinga
le measures. These results are obtained by adopting a technical filtration
enlargement and by constructing a universal aggregator of all arbitrage o
pportunities. We further introduce the notion of market feasibility and pr
ovide its characterization via arbitrage conditions. We conclude providing
a dual representation of Open Arbitrage in terms of weakly open sets of p
robability measures\, which highlights the robust nature of this concept.\
n\nhttps://indico.math.cnrs.fr/event/699/contributions/2375/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2375/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Chaotic Representation Property of Certain Families of Mart
ingales
DTSTART;VALUE=DATE-TIME:20150902T075000Z
DTEND;VALUE=DATE-TIME:20150902T083000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2376@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hans-Jürgen Engelbert (Friedrich Schiller-Universit
y of Jena)\nIn this talk\, we shall discuss the chaotic representation pro
perty for certain families of square integrable martingales. Our approach
extends well-known results on the Brownian motion or the compensated Poiss
on process in which case the family would only consist of a single marting
ale. The starting point for these investigations has been the problem of f
inding appropriate families of martingales related to Lévy processes sati
sfying the chaotic (or only predictable) representation property. In parti
cular\, we extend the results of Nualart and Schoutens on the chaotic repr
esentation property of the Teugels martingales. In the context of Mathemat
ical Finance\, families of martingales enjoying the chaotic (and hence pre
dictable) representation property can serve for the completion of an (inco
mplete) financial market. As a linear or geometric Lévy market is normall
y incomplete\, our approach can be applied to construct different completi
ons of the market\, in the sense that there will be added to the stock and
the bank account a certain family of contingent claims\, the terminal val
ues of the martingales from the family under consideration.\n\nhttps://ind
ico.math.cnrs.fr/event/699/contributions/2376/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2376/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malliavin differentiability of BSDEs
DTSTART;VALUE=DATE-TIME:20150904T085000Z
DTEND;VALUE=DATE-TIME:20150904T092000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2377@indico.math.cnrs.fr
DESCRIPTION:Speakers: ANTHONY REVEILLAC (INSA de Toulouse - Institut de Ma
thématiques de Toulouse)\nIn this talk we will revisit conditions under w
hich the solution to a BSDE is Malliavin differentiable. To this end\, we
provide a new characterization of the Malliavin-Sobolev spaces which is pa
rticularly suitable for our purpose. This talk is based on joint works wit
h Thibaut Mastrolia\, Peter Imkeller and Dylan Possamaï.\n\nhttps://indic
o.math.cnrs.fr/event/699/contributions/2377/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2377/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A martingale fixed-point problem in optimal reserve exploration
DTSTART;VALUE=DATE-TIME:20150903T092000Z
DTEND;VALUE=DATE-TIME:20150903T095000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2378@indico.math.cnrs.fr
DESCRIPTION:Speakers: Juri Hinz (UTS)\nA martingale fixed-point problem in
optimal reserve exploration\n\nWe show how diverse problems in the area
optimal resource management\, exploration of natural reserves\, and envi
ronmental protection by cap-and-trade mechanism can be naturally formulate
d under a unified framework\, as stochastic control problems of a specific
type. Moreover\, it turns out that solutions to these control problems
are equivalently described in terms of fixed-point equations for martinga
les. Such fixed point martingale processes can be interpreted as a marke
t price for a virtual\nallowance which gives the right to use the resource
s remaining in the reserve after the exploration. We suggest numerical sch
emes for solution of these fixed point equations and elaborate on their a
pplications.\n\nhttps://indico.math.cnrs.fr/event/699/contributions/2378/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2378/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evolution of models in evolving markets
DTSTART;VALUE=DATE-TIME:20150902T144000Z
DTEND;VALUE=DATE-TIME:20150902T151000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2379@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marek Musiela (Oxfor Man Institute)\nMathematical mo
dels are developed to capture market behaviour at a point in time and are
used to\ngain competitive advantage over time. In the option business\, fo
r example\, they are calibrated to\nliquid information and used to price a
nd trade more exotic and hence less liquid products. However\nmarket liqui
dity changes over time\, it can increase or evaporate depending on the eco
nomic\nconditions. This is one of the factors that drive evolution of mode
ls which need to be adapted to the\nchanging market conditions.\nIn this t
alk I will use the evolution of classical option pricing models as an exam
ple of the feedback\nloop: from academia to industry and back.\n\nhttps://
indico.math.cnrs.fr/event/699/contributions/2379/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2379/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Investment timing\, collateral\, and financing constraints
DTSTART;VALUE=DATE-TIME:20150902T155000Z
DTEND;VALUE=DATE-TIME:20150902T162000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2380@indico.math.cnrs.fr
DESCRIPTION:Speakers: Takashi Shibata (Tokyo Metropolitan University)\nhtt
ps://indico.math.cnrs.fr/event/699/contributions/2380/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2380/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brownian trading excursions
DTSTART;VALUE=DATE-TIME:20150901T095000Z
DTEND;VALUE=DATE-TIME:20150901T102000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2381@indico.math.cnrs.fr
DESCRIPTION:Speakers: Thorsten Rheinlander (TU Vienna)\nIn a model for the
limit order book with arrivals and cancellations\, we derive an SPDE with
one heating source and two cooling elements on a finite rod for the order
volume which we solve in terms of local time. Moreover\, via Brownian exc
ursion theory\, we provide a hyperbolic function table for the Laplace tra
nsforms of various times of trade. A bivariate Laplace-Mellin transform is
introduced for the joint excursion height and length and expressed in ter
ms of the Riemann Xi function. Finally\, we show that two diferent disinte
grations of the Ito measure are equivalent to Jacobi's Theta transformatio
n formula. \nThis is joint work with Friedrich Hubalek\, Paul Krühner an
d Sabine Sporer.\n\nhttps://indico.math.cnrs.fr/event/699/contributions/23
81/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2381/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Random Periodic Processes\, Periodic Measures and Ergodicity
DTSTART;VALUE=DATE-TIME:20150904T154000Z
DTEND;VALUE=DATE-TIME:20150904T162000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2382@indico.math.cnrs.fr
DESCRIPTION:Speakers: Huaizhong Zhao (Loughborough University)\nAn ergodic
theorem and a mean ergodic theorem in the random periodic regime on a Pol
ish space is proved. \nThe idea of Poincaré sections is introduced and un
der the strong Feller and irreducible assumptions on Poincaré \nsections\
, the weak convergence of the transition probabilities at the discrete tim
e of integral multiples of the period is \nobtained. Thus the Khas'minskii
-Doob type theorem is established and the ergodicity of the invariant meas
ure\, which \nis the mean of the periodic measure over a period interval\,
is obtained. The Krylov-Bogoliubov type theorem for the \nexistence of pe
riodic measures by considering the Markovian semigroup on a Poincaré sect
ion at discrete times of \nintegral multiples of the period is also proved
. It is proved that three equivalent criteria give necessary and sufficien
t \nconditions to classify between random periodic and stationary regimes.
The three equivalent criteria are given in terms \nof three different not
ion respectively\, namely Poincaré sections\, angle variable and infinite
simal generator of the induced \nlinear transformation of the canonical dy
namical system associated with the invariant measure. It is proved that in
finitesimal \ngenerator has only two simple eigenvalues\, which are $0$ an
d the quotient of $2\\pi$ by the minimal period\, while the \nclassical Ko
opman-von Neumann theorem says that the generator has only one simple eige
nvalue $0$ in the stationary \nand mixing case. The ``equivalence" of rand
om periodic processes and periodic measures is established.\nThe strong la
w of large numbers (SLLN) is also proved for random periodic processes. \n
\nThis is a joint work with Chunrong Feng.\n\nhttps://indico.math.cnrs.fr/
event/699/contributions/2382/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2382/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Risk Minimization under Mortality and Its Stochastics.
DTSTART;VALUE=DATE-TIME:20150901T092000Z
DTEND;VALUE=DATE-TIME:20150901T095000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2383@indico.math.cnrs.fr
DESCRIPTION:Speakers: Tahir Choulli (UNiversity of Alberta)\nIn this talk\
, I will present our contributions in two topics that complement each othe
r. The first topic deals with risk minimization when the mortality is take
n into consideration. For this theme\, we adopt the popular risk-minimizat
ion framework of Follmer and Sonderman. In this line of research\, we quan
tify the impact of the mortality uncertainty\, as well as the intrinsic ri
sk of its correlation with the financial market\, on the optimal risk-min
imizing strategy. These achievements is based essentially on new stochast
ic developments that sound tailored made for them. In this stochastic par
t\, which represents our second topic of contribution and originality\, we
obtained two principal results. On the one hand\, we introduced and analy
zed two new classes of martingales in the enlarged filtration. On the othe
r hand\, thanks to our new spaces of martingales\, we elaborated a complet
e\, precise and explicit optional decomposition for martingales of the lar
ge filtration stopped at the death time. This decomposition is vital in th
e analysis of the first topic if one wants to address fully the mortality
risk without excluding any mortality model and/or market model.\n\nThis ta
lk is based on joint works with Catherine Daveloose and Michele Vanmaele.\
n\nhttps://indico.math.cnrs.fr/event/699/contributions/2383/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2383/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agency\, Firm Growth and Managerial Turnover
DTSTART;VALUE=DATE-TIME:20150902T135000Z
DTEND;VALUE=DATE-TIME:20150902T143000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2384@indico.math.cnrs.fr
DESCRIPTION:Speakers: Mihail Zervos (London School of Economics)\nWe consi
der managerial incentive provision under moral hazard in a firm that is su
bject to stochastic growth opportunities. In the model that we study\, man
agers are dismissed after poor performance as well as when an opportunity
to improve the firm's profitability that requires a change of management a
rises. The optimal contract may induce managerial entrenchment\, whereby\,
ex post-attractive growth opportunities are foregone after good performan
ce because of contractual commitments. Realised growth depends on the freq
uency and size of growth opportunities as well as on the severity of moral
hazard. The prospect of growth-induced turnover limits the firm's ability
to rely on deferred compensation as a disciplinary device.\n\nhttps://ind
ico.math.cnrs.fr/event/699/contributions/2384/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2384/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Existence and uniqueness of viscosity solutions for second order i
ntegro-differential equations without monotonicity condition
DTSTART;VALUE=DATE-TIME:20150904T151000Z
DTEND;VALUE=DATE-TIME:20150904T154000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2385@indico.math.cnrs.fr
DESCRIPTION:Speakers: said hamadene (LMM\, Universite du Maine\, Le Mans\,
France)\nIn this talk\, we discuss a new existence and uniqueness result
of a continuous viscosity solution for integro-partial differential equati
on (IPDE in short). \n The novelty is that we relax the so-called monotoni
city assumption on the driver which is classically assumed in the literatu
re of viscosity solution of equation with a non local term. Our method is
based on the link of those IPDEs with backward stochastic differential equ
ations (BSDEs in short) with jumps for which we already know that the solu
tion exists and is unique.\n\nhttps://indico.math.cnrs.fr/event/699/contri
butions/2385/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2385/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Skorokhod embedding problem and FBSDE
DTSTART;VALUE=DATE-TIME:20150902T070000Z
DTEND;VALUE=DATE-TIME:20150902T074000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2386@indico.math.cnrs.fr
DESCRIPTION:Speakers: Peter Imkeller (Mathematisches Institut der Humboldt
-Universität zu Berlin)\nA link between martingale representation and sol
utions of the Skorokhod embedding problem has been established by R. Bass.
A generalization of his approach to FBSDE leads us to solutions of the Sk
orokhod embedding problem for diffusion processes with deterministic drift
. This is joint work with Alexander Fromm and David Prömel.\n\nhttps://in
dico.math.cnrs.fr/event/699/contributions/2386/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2386/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On optimal stopping with expectation constraints
DTSTART;VALUE=DATE-TIME:20150904T123000Z
DTEND;VALUE=DATE-TIME:20150904T130000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2387@indico.math.cnrs.fr
DESCRIPTION:Speakers: Stefan Ankirchner (University of jena)\nThe talk is
about optimal stopping with the contraint that the expectation of any stop
ping time has to be bounded by a given constant. We show that by introduci
ng a new state variable one can derive a dynamic programming principle. Th
is allows to characterize the value function as the solution of a PDE and
to obtain a verification theorem.\nFinally we compare our approach with al
ternative solution methods and discuss some examples.\n\nhttps://indico.ma
th.cnrs.fr/event/699/contributions/2387/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2387/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Degenerate Backward SPDE with Singular Terminal Value and Related
Applications in Mathematical Finance
DTSTART;VALUE=DATE-TIME:20150904T143000Z
DTEND;VALUE=DATE-TIME:20150904T150000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2388@indico.math.cnrs.fr
DESCRIPTION:Speakers: Qi Zhang (Fudan University)\nWe study the degenerate
backward stochastic partial differential equation with singular terminal
value\, and prove the existence and uniqueness of its non-negative solutio
n by the comparison theorem and the gradient estimate of solution. This ki
nd of equation has an application in the portfolio liquidation problem. Th
is is a joint work with Ulrich Horst and Jinniao Qiu.\n\nhttps://indico.ma
th.cnrs.fr/event/699/contributions/2388/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2388/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Multi-Dimensional Backward Stochastic Differential Equations of Di
agonally Quadratic generators
DTSTART;VALUE=DATE-TIME:20150904T135000Z
DTEND;VALUE=DATE-TIME:20150904T143000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2389@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ying Hu (Université Rennes 1)\nThe paper is concern
ed with adapted solution of a multi-dimensional BSDE with a "diagonally" q
uadratic generator\, the quadratic part of whose ith component only depend
s on the ith row of the second unknown variable. Local and global solution
s are given. In our proofs\, it is natural and crucial to apply both John-
Nirenberg and reverse H\\"older inequalities for BMO martingales.\n\nhttps
://indico.math.cnrs.fr/event/699/contributions/2389/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2389/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No arbitrage conditions in the multi-curve modelling of the term s
tructure of interest rates
DTSTART;VALUE=DATE-TIME:20150901T075000Z
DTEND;VALUE=DATE-TIME:20150901T083000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2391@indico.math.cnrs.fr
DESCRIPTION:Speakers: Wolfgang Runggaldier (University of Padova\, Diparti
mento di Matematica)\nThe context of the talk is the multi-curve modelling
of the term structure of interest rates as it arose after the big financi
al crisis. In particular\, we discuss possible extensions of the no-arbitr
age drift condition in an HJM framework.\n(Based on joint work with Zorana
Grbac)\n\nhttps://indico.math.cnrs.fr/event/699/contributions/2391/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2391/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dynamics of order positions and related queues in a limit order bo
ok
DTSTART;VALUE=DATE-TIME:20150901T120000Z
DTEND;VALUE=DATE-TIME:20150901T124000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2392@indico.math.cnrs.fr
DESCRIPTION:Speakers: xin guo (UC Berkeley)\nOne of the most rapidly growi
ng research areas in financial mathematics is centered around modeling LOB
dynamics and/or minimizing the inventory/execution risk with consideratio
n of microstructure of LOB. A critical yet missing piece of the puzzle\, i
s the dynamics of an order position in a LOB. \n\nIn this talk\, we will p
resent some of our recent progress regarding the limiting behavior of the
dynamics of order positions in a LOB. As a corollary\, we will present som
e explicit expressions for various quantities of interests\, including the
distribution of a particular limit order being executed by a given time\,
its expected value and variance. \n\nOur analysis builds on techniques an
d results from classical probability theory: the functional central limit
theorems of Glynn and Ward (1988) and Bullinski and Shashkin (2007)\, the
convergence of stochastic processes by Kurtz and Protter (1991)\, and the
sample path large deviation principle of Dembo and Zajic (1998). \n\nBased
on joint work with Z. Ruan (UC Berkeley) and L. J. Zhu (U. of Minnesota).
\n\nhttps://indico.math.cnrs.fr/event/699/contributions/2392/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2392/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A measure-valued SDE with applications to interest rates and stoch
astic volatility
DTSTART;VALUE=DATE-TIME:20150901T085000Z
DTEND;VALUE=DATE-TIME:20150901T092000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2393@indico.math.cnrs.fr
DESCRIPTION:Speakers: Michael Tehranchi (University of Cambridge)\nThis ta
lk will discuss a certain stochastic evolution equation in the space of pr
obability measures\, including existence and uniqueness results. A solutio
n of this equation gives rise\, in a natural way\, to an interest rate ter
m structure model\, in the same spirit as the Heath-Jarrow-Morton framewor
k. Furthermore\, such a measure-valued process gives rise to a market mod
el of the dynamics of the implied volatility surface\, at least under some
conditions.\n\nhttps://indico.math.cnrs.fr/event/699/contributions/2393/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2393/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rare event simulation related to financial risks: efficient estima
tion and sensitivity analysis
DTSTART;VALUE=DATE-TIME:20150903T075000Z
DTEND;VALUE=DATE-TIME:20150903T083000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2394@indico.math.cnrs.fr
DESCRIPTION:Speakers: Emmanuel Gobet (Po)\nWe develop the reversible shaki
ng transformation methods of Gobet and Liu (2014) to estimate the rare eve
nt probability arising in different financial risk settings driven by gene
ral Gaussian noise. The underlying Markov chains introduced in our approac
hes take values directly in the path space. We provide theoretical justifi
cation for few key properties of these Markov chains which are required fo
r their ergodicity. Further\, using these properties\, we prove consistenc
y results for the simulation estimator. The examples in our work cover usu
al semi-martingale stochastic models (not necessarily Markovian) driven by
Brownian motion\, and\, also fractional Brownian motion based models to a
ddress various financial risks. Our approach also handles the important pr
oblem of sensi- tivities of rare event probability. We compare our numeric
al studies to the already existing results and demonstrate improved comput
ational performance.\n(Joint work with A. Agarwal\, S. De Marco\, G. Liu.)
\n\nhttps://indico.math.cnrs.fr/event/699/contributions/2394/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2394/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Estimation Methods for Risk Measurement
DTSTART;VALUE=DATE-TIME:20150903T095000Z
DTEND;VALUE=DATE-TIME:20150903T102000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2395@indico.math.cnrs.fr
DESCRIPTION:Speakers: HASSAN OMIDI FIROUZI (LABEXREFI)\nBanks and financia
l institutions can use either the internal models-based approach or the s
tandardized approach to assess and report the risk of the trading book for
future periods. In this paper\, we examine relevant estimation methods fo
r computing Value at Risk (VaR) and Expected Shortfall (ES) for banks at b
oth desk level and bank-wide level. We provide a benchmark method for esti
mation and\nstudy financial and statistical properties of the method. We p
rovide numerical results for different hypothetical portfolios.\n\nhttps:/
/indico.math.cnrs.fr/event/699/contributions/2395/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2395/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joint distribution of spectrally negative Lévy process and its oc
cupation time\, with step option pricing in view
DTSTART;VALUE=DATE-TIME:20150902T094000Z
DTEND;VALUE=DATE-TIME:20150902T102000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2396@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hélène Guérin (IRMAR)\nWe are interested in the j
oint distribution of a spectrally negative Lévy process and its occupatio
n time when both are sampled at a fixed time. The result is expressed in t
erms of scale functions of the underlying process. \nThis result can be us
ed to price step options and the particular case of an exponential spectra
lly negative Lévy jump-diffusion will be presented.\n\nThis is a joint wo
rk with J.F. Renaud.\n\nhttps://indico.math.cnrs.fr/event/699/contribution
s/2396/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2396/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Continuity Problems in Boundary Crossing Problems
DTSTART;VALUE=DATE-TIME:20150901T151000Z
DTEND;VALUE=DATE-TIME:20150901T155000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2398@indico.math.cnrs.fr
DESCRIPTION:Speakers: Konstantin Borovkov (University of Melbourne)\nCompu
ting the probability for a given diffusion process to stay under a particu
lar boundary is crucial in many important applications including pricing f
inancial barrier options. It is a rather tedious task that\, in the genera
l case\, requires the use of some approximation methodology. One possible
approach to this problem is to approximate given (general curvilinear) bou
ndaries with some other boundaries\, of a form enabling one to relatively
easily compute the boundary crossing probability. We discuss results on th
e accuracy of such approximations for both the Brownian motion process and
general time-homogeneous diffusions\, their extensions to the multivariat
e case\, and also some contiguous topics.\n\nhttps://indico.math.cnrs.fr/e
vent/699/contributions/2398/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2398/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the dual problem of utility maximization in incomplete markets
DTSTART;VALUE=DATE-TIME:20150902T125000Z
DTEND;VALUE=DATE-TIME:20150902T133000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2399@indico.math.cnrs.fr
DESCRIPTION:Speakers: Yiqing LIN (University of Vienna)\nWe study the dual
problem of the expected utility maximization in incomplete markets with b
ounded random endowment. We start with the duality results of [Cvitanic-Sc
hachermayer-Wang\, 2001]\, in which the optimal strategy is obtained by fi
rst formulating and solving a dual problem. We observe that: in the Browni
an framework\, the countably additive part $Q^r$ of the dual optimizer $Q\
\in (L^\\infty)^*$ in the settings of [Cvitanic-Schachermayer-Wang\, 2001]
can be represented by the terminal value of a supermartingale deflator $Y
$ defined in [Kramkov-Schachermayer\, 1999]\, which moreover is a local ma
rtingale.\n\nhttps://indico.math.cnrs.fr/event/699/contributions/2399/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2399/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Information Asymmetries\, Volatility\, Liquidity\, and the Tobin T
ax
DTSTART;VALUE=DATE-TIME:20150901T135000Z
DTEND;VALUE=DATE-TIME:20150901T143000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2400@indico.math.cnrs.fr
DESCRIPTION:Speakers: Albina Danilova (LSE)\nInformation asymmetries and t
rading costs\, in a nancial market model with dynamic information\, genera
te a self-exciting equilibrium price process with stochastic volatility\,
even if news have constant volatility. Intuitively\, new (constant volatil
ity) information is released to the market at trading times that\, due to
traders' strategic choices\, dier from calendar times. This generates an e
ndogenous stochastic time change between trading and calendar times\, and
stochastic volatility of the price process in calendar time. In equilibriu
m: price volatility is autocorrelated and is a non-linear function of numb
er and volume of trades\; the relative informativeness of number and volum
e of trades depends on the data sampling frequency\; volatility\, the limi
t order book\, tightness\, depth\, resilience\, and trading activity\, are
jointly determined by information asymmetries and trading costs. Our clos
ed form solutions rationalize a large set of empirical evidence and\nprovi
de a natural laboratory for analyzing the equilibrium eects of a nancial\n
transaction tax.\n\nhttps://indico.math.cnrs.fr/event/699/contributions/24
00/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2400/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polynomial preserving processes and discrete-tenor interest rate m
odels
DTSTART;VALUE=DATE-TIME:20150901T143000Z
DTEND;VALUE=DATE-TIME:20150901T150000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2401@indico.math.cnrs.fr
DESCRIPTION:Speakers: Zorana Grbac (Université Paris Diderot)\nThe class
of polynomial preserving Markov processes has proved to be very suitable f
or modeling purposes in mathematical finance due to its flexibility and an
alytical tractability\, which allows to obtain closed/semi-closed pricing
formulas for various derivatives. In this work we focus on an application
of this class for interest rate models on a discrete tenor. Here the polyn
omial preserving property of the driving process is key already in the mod
el construction which is based on polynomial functions. This includes Libo
r-type models\, as well as extensions to the multiple-curve term structure
. The main advantage of this model class is the possibility to obtain at t
he same time semi-analytic pricing formulas for both caplets and swaptions
that do not require any approximations. Moreover\, additive constructions
allow to easily ensure\, if desired\, properties such as positivity of in
terest rates and spreads and monotonicity of spreads with respect to the t
enor - in view of the current market situation a model in which the refere
nce OIS interest rates can become negative and the spreads still remain po
sitive is of particular interest.\nWe conclude by presenting a model speci
fication driven by a Lévy-type polynomial preserving process and a corres
ponding Fourier transform formula used in pricing of caplets and swaptions
. \nThis is joint work with K. Glau and M. Keller-Ressel.\n\nhttps://indic
o.math.cnrs.fr/event/699/contributions/2401/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2401/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Recent development in martingale optimal transport
DTSTART;VALUE=DATE-TIME:20150903T070000Z
DTEND;VALUE=DATE-TIME:20150903T074000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2402@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nizar Touzi (Ecole Polytechnique)\nWe study the opti
mal transport between two probability measures on the real line\, where th
e transport plans are laws of one-step martingales. A quasi-sure formulati
on of the dual problem is introduced and shown to yield a complete duality
theory for general marginals and measurable reward (cost) functions: abse
nce of a duality gap and existence of dual optimizers. Both properties are
shown to fail in the classical formulation. As a consequence of the duali
ty result\, we obtain a general principle of cyclical monotonicity describ
ing the geometry of optimal transports.\n\nhttps://indico.math.cnrs.fr/eve
nt/699/contributions/2402/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2402/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grossissement de filtration en temps discret
DTSTART;VALUE=DATE-TIME:20150901T125000Z
DTEND;VALUE=DATE-TIME:20150901T133000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2403@indico.math.cnrs.fr
DESCRIPTION:Speakers: Monique Jeanblanc (université Evry Val d'ESSONNE)\n
Nous étudions le cas de grossissement de filtration en temps discret et\
nobtenons très simplement les formules connues en temps continu. L'expos
é a un but essentiellement pédagogique.\n\nhttps://indico.math.cnrs.fr/
event/699/contributions/2403/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2403/
END:VEVENT
BEGIN:VEVENT
SUMMARY:General one-dimensional diffusion: characterization\, optimal stop
ping problem
DTSTART;VALUE=DATE-TIME:20150904T120000Z
DTEND;VALUE=DATE-TIME:20150904T123000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2404@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ernst Presman (CEMI RAN)\nThe talk is devoted to the
general one-dimensional diffusion. We discuss the definition and characte
rization of such processes: scale\, speed measure\, killing measure. The g
enerating operator is considered on an extended space of functions (as com
pared with a classical approach). We give a local characterization potenti
al functions and excessive functions. For the general one-dimensional diff
usion we give a necessary and sufficient conditions that the optimal stra
tegy in the optimal stopping problem has a threshold or an island characte
r.\n\nhttps://indico.math.cnrs.fr/event/699/contributions/2404/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2404/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sensitivity Analysis in Lévy Fixed Income Theory
DTSTART;VALUE=DATE-TIME:20150902T085000Z
DTEND;VALUE=DATE-TIME:20150902T093000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2405@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ernst Eberlein (University of Freiburg)\nA brief int
roduction into the Lévy Libor and the Lévy forward process model is give
n. Basic properties of these two frameworks are discussed. The main goal i
s to derive formulas for price sensitivities of standard fixed income deri
vatives. Two approaches are discussed. The first approach is based on the
integration–by–parts formula\, which lies at the core of the applicati
on of the Malliavin calculus to finance. The second approach consists in u
sing Fourier based methods for pricing derivatives. We illustrate the resu
lt by applying the formulas to a caplet price where the underlying model i
s driven by a time–inhomogeneous Gamma process and alternatively by a Va
riance Gamma process. A comparison between the two approaches which come f
rom totally different mathematical fields is made.\nThis is joint work wit
h M'hamed Eddahbi and Sidi Mohamed Lalaoui\n\nhttps://indico.math.cnrs.fr/
event/699/contributions/2405/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2405/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Variational View to Optimal Stopping with Application to Real Opti
ons
DTSTART;VALUE=DATE-TIME:20150904T130000Z
DTEND;VALUE=DATE-TIME:20150904T133000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2406@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexander Slastnikov (CEMI)\nWe describe a variation
al approach to solving optimal stopping problems for diffusion processes.
In the framework of this approach\, one can find optimal stopping time ove
r the class of first exit time from the set (for a given family of sets).
For the case of one-parametric family of sets we give necessary and suffic
ient conditions for optimality of stopping time over this class.\nFor one-
dimensional diffusion processes and two families of `semi-intervals’\, w
e set necessary and sufficient conditions under which the optimal stopping
time has a threshold structure.\nWe study smooth pasting condition from a
variational view\, present some examples when the solution to the free-bo
undary problem is not the solution to the optimal stopping problem\, and g
ive some results about a relation between solutions to free-boundary probl
em and optimal stopping problem. At last\, some applications of these resu
lts to both investment timing and optimal abandonment models are considere
d.\n\nhttps://indico.math.cnrs.fr/event/699/contributions/2406/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2406/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Multidimensional quadratic BSDEs with separated generators
DTSTART;VALUE=DATE-TIME:20150904T092000Z
DTEND;VALUE=DATE-TIME:20150904T095000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2407@indico.math.cnrs.fr
DESCRIPTION:Speakers: Peng Luo (University of Konstanz)\nWe consider multi
dimensional quadratic BSDEs with generators which can be separated into a
coupled and an uncoupled part which allows to analyse the degree of coupli
ng of the system in terms of the growth coefficients. We provide condition
s on the relationship between the size of the terminal condition and the d
egree of coupling which guarantee existence and uniqueness of solutions.\n
\nhttps://indico.math.cnrs.fr/event/699/contributions/2407/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2407/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A result on integral functionals with infinitely many constraints
DTSTART;VALUE=DATE-TIME:20150902T120000Z
DTEND;VALUE=DATE-TIME:20150902T124000Z
DTSTAMP;VALUE=DATE-TIME:20210416T202856Z
UID:indico-contribution-699-2408@indico.math.cnrs.fr
DESCRIPTION:Speakers: Martin Schweizer (ETH Zurich)\nA classic result (due
to Borwein and Lewis) in the theory of optimisation under constraints say
s the following. Suppose we have n measurable functions a_i in L^q on a fi
nite measure space and a nonnegative function x in L^p. Call b_i the integ
rals of x against a_i. Then there exists a function z in the norm interior
of L^infty which has the same integrals b_i against a_i as x. So if the c
onstraints given by the a_i are feasible in L^p_+\, they are also feasible
in L^infty_{++}.\n\nWe present an extension of this result to a setting w
ith infinitely many\, measurably parametrised constraints\, and we show ho
w this comes up and can be used in arbitrage theory.\n\nThis is based on j
oint work with Tahir Choulli (University of Alberta\, Edmonton).\n\nhttps:
//indico.math.cnrs.fr/event/699/contributions/2408/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/699/contributions/2408/
END:VEVENT
END:VCALENDAR