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BEGIN:VEVENT
SUMMARY:Group solvency tests\, intragroup transfers and intragroup diversi
fication: a set-valued perspective
DTSTART:20150903T085000Z
DTEND:20150903T092000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2369@indico.math.cnrs.fr
DESCRIPTION:Speakers: Andreas Haier (University of Berne)\, Ilya Molchanov
(University of Berne)\, Michael Schmutz (University of Berne)\n\nThe aim
of risk-based solvency frameworks\, such as Solvency II to be introduced i
n the EU and the Swiss Solvency Test (SST) that has been in force in Switz
erland since 2011\, is to assess the financial health of insurance compani
es. This is achieved by quantifying capital adequacy by calculating the so
lvency capital requirement (SCR). These calculations are based on scalar r
isk measures. Assessing the financial health of insurance groups (of sever
al connected companies) is an even more challenging task\; a variety of ap
proaches can be taken to tackle the issue. Aspects of the most well-known
approaches\, and modified versions of them\, are discussed based on a set-
valued 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:20150904T070000Z
DTEND:20150904T074000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2370@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nicole El Karoui (UPMC)\n\nWe consider the non-Bayes
ian quickest detection problem of an unobservable time\nof change in the r
ate of an inhomogeneous Poisson process. We seek a stopping\nrule that min
imizes the robust Lorden criterion. The latter is formulated in terms\nof
the number of events until detection\, both for the worst-case delay and t
he false\nalarm constraint. In the Wiener case\, such a problem was solved
using the so-\ncalled cumulative sums (cusum) strategy by many authors (M
oustakides (2004)\,\nor Shyraiev (1963\,..2009)). In our setting\, we deri
ve the exact optimality of the\ncusum stopping rule by using finite variat
ion calculus and elementary martingale\nproperties to characterize the per
formance functions of the cusum stopping rule in\nterms of scale function.
These are solutions of some delayed differential equations\nthat we solve
elementary. The case of detecting a decrease in the intensity is easy to\
nstudy because the performance functions are continuous. In case of increa
se where\nthe performance functions are not continuous\, martingale proper
ties require using a\ndiscontinuous local time. Nevertheless\, from an ide
ntity relating the scale functions\,\nthe optimality of the cusum rule sti
ll holds. Numerical applications are provided.\nThis is joint work with S.
Loisel (ISFA) and Y.Sahli (ISFA).\n\nhttps://indico.math.cnrs.fr/event/699
/contributions/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:20150904T095000Z
DTEND:20150904T102000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2371@indico.math.cnrs.fr
DESCRIPTION:Speakers: Gordan Zitkovic (University of Texas at Austin)\, Ko
stas Kardaras (London School of Economics)\, Hao Xing (London School of Ec
onomics)\n\nWe tackle a number of problems related to the existence of con
tinuous-time stochastic Radner equilibria with incomplete markets. Various
assumptions of "smallness" type-including a new notion of "closeness to P
areto optimality"-are shown to be sufficient for existence and uniqueness.
Central role in our analysis is played by a fully-coupled nonlinear syste
m of quadratic BSDEs.\n\nThis is a joint work with Kostas Kardaras and Gor
dan 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:20150902T162000Z
DTEND:20150902T165000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2372@indico.math.cnrs.fr
DESCRIPTION:Speakers: Mikhail Zhitlukhin (Steklov Mathematical institute)\
n\nThis paper studies the expected value of the supremum of fractional Bro
wnian motion and related Gaussian processes. We obtain upper and lower bou
nds for the expected supremum and bounds for the approximation of the supr
emum of a continuous process by random walks. As corollaries\, we obtain r
esults on the structure of fractional Brownian motion when the Hurst param
eter H tends to zero.\nThis is a joint work with Konstantin Borovkov\, Yul
ia Mishura and Alexander Novikov.\n\nhttps://indico.math.cnrs.fr/event/699
/contributions/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:20150904T075000Z
DTEND:20150904T083000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2373@indico.math.cnrs.fr
DESCRIPTION:Speakers: Masaaki Kijima (Tokyo Metropolitan University)\n\nTh
is paper proposes a unified approximation method for various options whose
payoffs depend on the volume weighted average price (VWAP). Despite their
popularity in practice\, quite few pricing models have been developed in
the literature. Also\, in previous works\, the underlying asset process ha
s been restricted to a geometric Brownian motion. In contrast\, our method
is applicable to the general class of continuous Markov processes such as
local volatility models\, stochastic volatility models\, and their combin
ations. Moreover\, our method can be used for any type of VWAP options wit
h fixed-strike\, floating-strike\, continuously sampled\, discretely sampl
ed\, forward-start\, and in-progress transactions. (joint work with H. Fun
ahashi)\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:20150902T151000Z
DTEND:20150902T154000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2374@indico.math.cnrs.fr
DESCRIPTION:Speakers: Kyoko Yagi (Faculty of Systems Science and Technolog
y\, Akita Prefectural University)\, Teruyoshi Suzuki (Hokkaido University)
\n\nWe analyze the interaction of the debt renegotiation between two firms
that cross-hold their issuing debts and equities. When the firms are reci
procally the major shareholder and/or debt holder of the other firms\, the
possibility of debt renegotiation will affect each other. We first develo
p models of debt renegotiation scheme: debt equity swap and strategic debt
service with game-theoretic setting under continuous time models. We then
derive the optimal boundaries in each model to offer debt renegotiation b
y 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 present the comparative statics of the renegotiation boundar
ies.\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:20150901T070000Z
DTEND:20150901T074000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2375@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marco Maggis (Università degli Studi di Milano)\, M
arco Burzoni (Università degli Studi di Milano)\, Marco Frittelli (Univer
sità degli Studi di Milano)\n\nIn a model independent discrete time finan
cial market\, we discuss the richness of the family of martingale measures
in relation to different notions of Arbitrage\, generated by a class S of
significant sets\, which we call Arbitrage de la classe S. The choice of
S reflects into the intrinsic properties of the class of polar sets of mar
tingale measures. In particular: for S = {Ω}\, absence of Model Independe
nt Arbitrage is equivalent to the existence of a martingale measure\; for
S being the open sets\, absence of Open Arbitrage is equivalent to the exi
stence of full support martingale measures. These results are obtained by
adopting a technical filtration enlargement and by constructing a universa
l aggregator of all arbitrage opportunities. We further introduce the noti
on of market feasibility and provide its characterization via arbitrage co
nditions. We conclude providing a dual representation of Open Arbitrage in
terms of weakly open sets of probability measures\, which highlights the
robust nature of this concept.\n\nhttps://indico.math.cnrs.fr/event/699/co
ntributions/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:20150902T075000Z
DTEND:20150902T083000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2376@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hans-Jürgen Engelbert (Friedrich Schiller-Universit
y of Jena)\n\nIn this talk\, we shall discuss the chaotic representation p
roperty for certain families of square integrable martingales. Our approac
h extends well-known results on the Brownian motion or the compensated Poi
sson process in which case the family would only consist of a single marti
ngale. The starting point for these investigations has been the problem of
finding appropriate families of martingales related to Lévy processes sa
tisfying the chaotic (or only predictable) representation property. In par
ticular\, we extend the results of Nualart and Schoutens on the chaotic re
presentation property of the Teugels martingales. In the context of Mathem
atical Finance\, families of martingales enjoying the chaotic (and hence p
redictable) representation property can serve for the completion of an (in
complete) financial market. As a linear or geometric Lévy market is norma
lly incomplete\, our approach can be applied to construct different comple
tions of the market\, in the sense that there will be added to the stock a
nd the bank account a certain family of contingent claims\, the terminal v
alues of the martingales from the family under consideration.\n\nhttps://i
ndico.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:20150904T085000Z
DTEND:20150904T092000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2377@indico.math.cnrs.fr
DESCRIPTION:Speakers: ANTHONY REVEILLAC (INSA de Toulouse - Institut de Ma
thématiques de Toulouse)\n\nIn this talk we will revisit conditions under
which the solution to a BSDE is Malliavin differentiable. To this end\, w
e provide a new characterization of the Malliavin-Sobolev spaces which is
particularly suitable for our purpose. This talk is based on joint works w
ith Thibaut Mastrolia\, Peter Imkeller and Dylan Possamaï.\n\nhttps://ind
ico.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:20150903T092000Z
DTEND:20150903T095000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2378@indico.math.cnrs.fr
DESCRIPTION:Speakers: Juri Hinz (UTS)\n\nA martingale fixed-point problem
in optimal reserve exploration\n\nWe show how diverse problems in the are
a optimal resource management\, exploration of natural reserves\, and en
vironmental protection by cap-and-trade mechanism can be naturally formula
ted under a unified framework\, as stochastic control problems of a specif
ic type. Moreover\, it turns out that solutions to these control problem
s are equivalently described in terms of fixed-point equations for martin
gales. Such fixed point martingale processes can be interpreted as a mar
ket price for a virtual\nallowance which gives the right to use the resour
ces remaining in the reserve after the exploration. We suggest numerical s
chemes for solution of these fixed point equations and elaborate on their
applications.\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:20150902T144000Z
DTEND:20150902T151000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2379@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marek Musiela (Oxfor Man Institute)\n\nMathematical
models are developed to capture market behaviour at a point in time and ar
e used to\ngain competitive advantage over time. In the option business\,
for example\, they are calibrated to\nliquid information and used to price
and trade more exotic and hence less liquid products. However\nmarket liq
uidity changes over time\, it can increase or evaporate depending on the e
conomic\nconditions. This is one of the factors that drive evolution of mo
dels which need to be adapted to the\nchanging market conditions.\nIn this
talk I will use the evolution of classical option pricing models as an ex
ample 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:20150902T155000Z
DTEND:20150902T162000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2380@indico.math.cnrs.fr
DESCRIPTION:Speakers: Takashi Shibata (Tokyo Metropolitan University)\n\nh
ttps://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:20150901T095000Z
DTEND:20150901T102000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2381@indico.math.cnrs.fr
DESCRIPTION:Speakers: Thorsten Rheinlander (TU Vienna)\n\nIn a model for t
he limit order book with arrivals and cancellations\, we derive an SPDE wi
th one heating source and two cooling elements on a finite rod for the ord
er volume which we solve in terms of local time. Moreover\, via Brownian e
xcursion theory\, we provide a hyperbolic function table for the Laplace t
ransforms of various times of trade. A bivariate Laplace-Mellin transform
is introduced for the joint excursion height and length and expressed in t
erms of the Riemann Xi function. Finally\, we show that two diferent disin
tegrations of the Ito measure are equivalent to Jacobi's Theta transformat
ion formula. \nThis is joint work with Friedrich Hubalek\, Paul Krühner
and Sabine Sporer.\n\nhttps://indico.math.cnrs.fr/event/699/contributions/
2381/
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:20150904T154000Z
DTEND:20150904T162000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2382@indico.math.cnrs.fr
DESCRIPTION:Speakers: Huaizhong Zhao (Loughborough University)\n\nAn ergod
ic theorem and a mean ergodic theorem in the random periodic regime on a P
olish space is proved. \nThe idea of Poincaré sections is introduced and
under the strong Feller and irreducible assumptions on Poincaré \nsection
s\, the weak convergence of the transition probabilities at the discrete t
ime of integral multiples of the period is \nobtained. Thus the Khas'minsk
ii-Doob type theorem is established and the ergodicity of the invariant me
asure\, which \nis the mean of the periodic measure over a period interval
\, is obtained. The Krylov-Bogoliubov type theorem for the \nexistence of
periodic measures by considering the Markovian semigroup on a Poincaré se
ction at discrete times of \nintegral multiples of the period is also prov
ed. It is proved that three equivalent criteria give necessary and suffici
ent \nconditions to classify between random periodic and stationary regime
s. The three equivalent criteria are given in terms \nof three different n
otion respectively\, namely Poincaré sections\, angle variable and infini
tesimal generator of the induced \nlinear transformation of the canonical
dynamical system associated with the invariant measure. It is proved that
infinitesimal \ngenerator has only two simple eigenvalues\, which are $0$
and the quotient of $2\\pi$ by the minimal period\, while the \nclassical
Koopman-von Neumann theorem says that the generator has only one simple ei
genvalue $0$ in the stationary \nand mixing case. The ``equivalence" of ra
ndom periodic processes and periodic measures is established.\nThe strong
law 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.f
r/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:20150901T092000Z
DTEND:20150901T095000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2383@indico.math.cnrs.fr
DESCRIPTION:Speakers: Tahir Choulli (UNiversity of Alberta)\n\nIn this tal
k\, I will present our contributions in two topics that complement each ot
her. The first topic deals with risk minimization when the mortality is ta
ken into consideration. For this theme\, we adopt the popular risk-minimiz
ation framework of Follmer and Sonderman. In this line of research\, we qu
antify the impact of the mortality uncertainty\, as well as the intrinsic
risk of its correlation with the financial market\, on the optimal risk-m
inimizing strategy. These achievements is based essentially on new stocha
stic developments that sound tailored made for them. In this stochastic p
art\, which represents our second topic of contribution and originality\,
we obtained two principal results. On the one hand\, we introduced and ana
lyzed two new classes of martingales in the enlarged filtration. On the ot
her hand\, thanks to our new spaces of martingales\, we elaborated a compl
ete\, precise and explicit optional decomposition for martingales of the l
arge filtration stopped at the death time. This decomposition is vital in
the analysis of the first topic if one wants to address fully the mortalit
y risk without excluding any mortality model and/or market model.\n\nThis
talk 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:20150902T135000Z
DTEND:20150902T143000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2384@indico.math.cnrs.fr
DESCRIPTION:Speakers: Stephane Guibaud (SciencesPo)\, M. Cecilia Bustamant
e (University of Maryland)\, Ronald W. Anderson (London School of Economic
s)\, Mihail Zervos (London School of Economics)\n\nWe consider managerial
incentive provision under moral hazard in a firm that is subject to stocha
stic growth opportunities. In the model that we study\, managers are dismi
ssed after poor performance as well as when an opportunity to improve the
firm's profitability that requires a change of management arises. The opti
mal contract may induce managerial entrenchment\, whereby\, ex post-attrac
tive growth opportunities are foregone after good performance because of c
ontractual commitments. Realised growth depends on the frequency and size
of growth opportunities as well as on the severity of moral hazard. The pr
ospect of growth-induced turnover limits the firm's ability to rely on def
erred compensation as a disciplinary device.\n\nhttps://indico.math.cnrs.f
r/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:20150904T151000Z
DTEND:20150904T154000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2385@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marie-Amélis Morlais (LMM\, University of Maine\, L
e Mans\, F.)\, said hamadene (LMM\, Universite du Maine\, Le Mans\, France
)\n\nIn this talk\, we discuss a new existence and uniqueness result of a
continuous viscosity solution for integro-partial differential equation (I
PDE in short). \n The novelty is that we relax the so-called monotonicity
assumption on the driver which is classically assumed in the literature of
viscosity solution of equation with a non local term. Our method is based
on the link of those IPDEs with backward stochastic differential equation
s (BSDEs in short) with jumps for which we already know that the solution
exists and is unique.\n\nhttps://indico.math.cnrs.fr/event/699/contributio
ns/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:20150902T070000Z
DTEND:20150902T074000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2386@indico.math.cnrs.fr
DESCRIPTION:Speakers: Peter Imkeller (Mathematisches Institut der Humboldt
-Universität zu Berlin)\n\nA link between martingale representation and s
olutions of the Skorokhod embedding problem has been established by R. Bas
s. A generalization of his approach to FBSDE leads us to solutions of the
Skorokhod embedding problem for diffusion processes with deterministic dri
ft. This is joint work with Alexander Fromm and David Prömel.\n\nhttps://
indico.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:20150904T123000Z
DTEND:20150904T130000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2387@indico.math.cnrs.fr
DESCRIPTION:Speakers: Stefan Ankirchner (University of jena)\n\nThe talk i
s about optimal stopping with the contraint that the expectation of any st
opping time has to be bounded by a given constant. We show that by introdu
cing a new state variable one can derive a dynamic programming principle.
This allows to characterize the value function as the solution of a PDE an
d to obtain a verification theorem.\nFinally we compare our approach with
alternative solution methods and discuss some examples.\n\nhttps://indico.
math.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:20150904T143000Z
DTEND:20150904T150000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2388@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jinniao Qiu (Humboldt University of Berlin)\, Ulrich
Horst (Humboldt University of Berlin)\, Qi Zhang (Fudan University)\n\nWe
study the degenerate backward stochastic partial differential equation wi
th singular terminal value\, and prove the existence and uniqueness of its
non-negative solution by the comparison theorem and the gradient estimate
of solution. This kind of equation has an application in the portfolio li
quidation problem. This is a joint work with Ulrich Horst and Jinniao Qiu.
\n\nhttps://indico.math.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:20150904T135000Z
DTEND:20150904T143000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2389@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ying Hu (Université Rennes 1)\n\nThe paper is conce
rned with adapted solution of a multi-dimensional BSDE with a "diagonally"
quadratic generator\, the quadratic part of whose ith component only depe
nds on the ith row of the second unknown variable. Local and global soluti
ons are given. In our proofs\, it is natural and crucial to apply both Joh
n-Nirenberg and reverse H\\"older inequalities for BMO martingales.\n\nhtt
ps://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:20150901T075000Z
DTEND:20150901T083000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2391@indico.math.cnrs.fr
DESCRIPTION:Speakers: Wolfgang Runggaldier (University of Padova\, Diparti
mento di Matematica)\n\nThe context of the talk is the multi-curve modelli
ng of the term structure of interest rates as it arose after the big finan
cial crisis. In particular\, we discuss possible extensions of the no-arbi
trage drift condition in an HJM framework.\n(Based on joint work with Zora
na 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:20150901T120000Z
DTEND:20150901T124000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2392@indico.math.cnrs.fr
DESCRIPTION:Speakers: xin guo (UC Berkeley)\n\nOne of the most rapidly gro
wing research areas in financial mathematics is centered around modeling L
OB dynamics and/or minimizing the inventory/execution risk with considerat
ion of microstructure of LOB. A critical yet missing piece of the puzzle\,
is the dynamics of an order position in a LOB. \n\nIn this talk\, we will
present some of our recent progress regarding the limiting behavior of th
e dynamics of order positions in a LOB. As a corollary\, we will present s
ome explicit expressions for various quantities of interests\, including t
he distribution of a particular limit order being executed by a given time
\, its expected value and variance. \n\nOur analysis builds on techniques
and results from classical probability theory: the functional central limi
t theorems of Glynn and Ward (1988) and Bullinski and Shashkin (2007)\, th
e convergence of stochastic processes by Kurtz and Protter (1991)\, and th
e sample path large deviation principle of Dembo and Zajic (1998). \n\nBas
ed 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:20150901T085000Z
DTEND:20150901T092000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2393@indico.math.cnrs.fr
DESCRIPTION:Speakers: Si Cheng (University of Cambridge)\, Michael Tehranc
hi (University of Cambridge)\n\nThis talk will discuss a certain stochasti
c evolution equation in the space of probability measures\, including exis
tence and uniqueness results. A solution of this equation gives rise\, in
a natural way\, to an interest rate term structure model\, in the same spi
rit as the Heath-Jarrow-Morton framework. Furthermore\, such a measure-va
lued process gives rise to a market model of the dynamics of the implied v
olatility 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:20150903T075000Z
DTEND:20150903T083000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2394@indico.math.cnrs.fr
DESCRIPTION:Speakers: Emmanuel Gobet (Po)\n\nWe develop the reversible sha
king transformation methods of Gobet and Liu (2014) to estimate the rare e
vent probability arising in different financial risk settings driven by ge
neral Gaussian noise. The underlying Markov chains introduced in our appro
aches take values directly in the path space. We provide theoretical justi
fication for few key properties of these Markov chains which are required
for their ergodicity. Further\, using these properties\, we prove consiste
ncy results for the simulation estimator. The examples in our work cover u
sual semi-martingale stochastic models (not necessarily Markovian) driven
by Brownian motion\, and\, also fractional Brownian motion based models to
address various financial risks. Our approach also handles the important
problem of sensi- tivities of rare event probability. We compare our numer
ical studies to the already existing results and demonstrate improved comp
utational 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:20150903T095000Z
DTEND:20150903T102000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2395@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jean-Paul Laurent (Université Paris 1 Panthéon-Sor
bonne)\, HASSAN OMIDI FIROUZI (LABEXREFI)\n\nBanks and financial instituti
ons can use either the internal models-based approach or the standardized
approach to assess and report the risk of the trading book for future per
iods. In this paper\, we examine relevant estimation methods for computing
Value at Risk (VaR) and Expected Shortfall (ES) for banks at both desk le
vel and bank-wide level. We provide a benchmark method for estimation and\
nstudy financial and statistical properties of the method. We provide nume
rical results for different hypothetical portfolios.\n\nhttps://indico.mat
h.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:20150902T094000Z
DTEND:20150902T102000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2396@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jean-François Renaud (UQÀM)\, Hélène Guérin (IR
MAR)\n\nWe are interested in the joint distribution of a spectrally negati
ve Lévy process and its occupation time when both are sampled at a fixed
time. The result is expressed in terms of scale functions of the underlyin
g process. \nThis result can be used to price step options and the particu
lar case of an exponential spectrally negative Lévy jump-diffusion will b
e presented.\n\nThis is a joint work with J.F. Renaud.\n\nhttps://indico.m
ath.cnrs.fr/event/699/contributions/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:20150901T151000Z
DTEND:20150901T155000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2398@indico.math.cnrs.fr
DESCRIPTION:Speakers: Konstantin Borovkov (University of Melbourne)\n\nCom
puting the probability for a given diffusion process to stay under a parti
cular boundary is crucial in many important applications including pricing
financial barrier options. It is a rather tedious task that\, in the gene
ral case\, requires the use of some approximation methodology. One possibl
e approach to this problem is to approximate given (general curvilinear) b
oundaries with some other boundaries\, of a form enabling one to relativel
y easily compute the boundary crossing probability. We discuss results on
the accuracy of such approximations for both the Brownian motion process a
nd general time-homogeneous diffusions\, their extensions to the multivari
ate case\, and also some contiguous topics.\n\nhttps://indico.math.cnrs.fr
/event/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:20150902T125000Z
DTEND:20150902T133000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2399@indico.math.cnrs.fr
DESCRIPTION:Speakers: Lingqi Gu (University of Vienna)\, Junjian YANG (Uni
versity of Vienna)\, Yiqing LIN (University of Vienna)\n\nWe study the dua
l problem of the expected utility maximization in incomplete markets with
bounded random endowment. We start with the duality results of [Cvitanic-S
chachermayer-Wang\, 2001]\, in which the optimal strategy is obtained by f
irst formulating and solving a dual problem. We observe that: in the Brown
ian 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 m
artingale.\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:20150901T135000Z
DTEND:20150901T143000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2400@indico.math.cnrs.fr
DESCRIPTION:Speakers: Christian Julliard (LSE\, Department of Finance)\, A
lbina Danilova (LSE)\n\nInformation asymmetries and trading costs\, in a n
ancial market model with dynamic information\, generate a self-exciting eq
uilibrium price process with stochastic volatility\, even if news have con
stant volatility. Intuitively\, new (constant volatility) information is r
eleased to the market at trading times that\, due to traders' strategic ch
oices\, dier from calendar times. This generates an endogenous stochastic
time change between trading and calendar times\, and stochastic volatility
of the price process in calendar time. In equilibrium: price volatility i
s autocorrelated and is a non-linear function of number and volume of trad
es\; the relative informativeness of number and volume of trades depends o
n the data sampling frequency\; volatility\, the limit order book\, tightn
ess\, depth\, resilience\, and trading activity\, are jointly determined b
y information asymmetries and trading costs. Our closed form solutions rat
ionalize a large set of empirical evidence and\nprovide a natural laborato
ry for analyzing the equilibrium eects of a nancial\ntransaction tax.\n\nh
ttps://indico.math.cnrs.fr/event/699/contributions/2400/
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:20150901T143000Z
DTEND:20150901T150000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2401@indico.math.cnrs.fr
DESCRIPTION:Speakers: Zorana Grbac (Université Paris Diderot)\n\nThe clas
s of polynomial preserving Markov processes has proved to be very suitable
for modeling purposes in mathematical finance due to its flexibility and
analytical tractability\, which allows to obtain closed/semi-closed pricin
g formulas for various derivatives. In this work we focus on an applicatio
n of this class for interest rate models on a discrete tenor. Here the pol
ynomial preserving property of the driving process is key already in the m
odel construction which is based on polynomial functions. This includes Li
bor-type models\, as well as extensions to the multiple-curve term structu
re. The main advantage of this model class is the possibility to obtain at
the same time semi-analytic pricing formulas for both caplets and swaptio
ns that do not require any approximations. Moreover\, additive constructio
ns allow to easily ensure\, if desired\, properties such as positivity of
interest rates and spreads and monotonicity of spreads with respect to the
tenor - in view of the current market situation a model in which the refe
rence OIS interest rates can become negative and the spreads still remain
positive is of particular interest.\nWe conclude by presenting a model spe
cification driven by a Lévy-type polynomial preserving process and a corr
esponding Fourier transform formula used in pricing of caplets and swaptio
ns. \nThis is joint work with K. Glau and M. Keller-Ressel.\n\nhttps://ind
ico.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:20150903T070000Z
DTEND:20150903T074000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2402@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nizar Touzi (Ecole Polytechnique)\n\nWe study the op
timal transport between two probability measures on the real line\, where
the transport plans are laws of one-step martingales. A quasi-sure formula
tion of the dual problem is introduced and shown to yield a complete duali
ty theory for general marginals and measurable reward (cost) functions: ab
sence of a duality gap and existence of dual optimizers. Both properties a
re shown to fail in the classical formulation. As a consequence of the dua
lity result\, we obtain a general principle of cyclical monotonicity descr
ibing the geometry of optimal transports.\n\nhttps://indico.math.cnrs.fr/e
vent/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:20150901T125000Z
DTEND:20150901T133000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2403@indico.math.cnrs.fr
DESCRIPTION:Speakers: Monique Jeanblanc (université Evry Val d'ESSONNE)\n
\nNous étudions le cas de grossissement de filtration en temps discret e
t\nobtenons très simplement les formules connues en temps continu. L'expo
sé 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:20150904T120000Z
DTEND:20150904T123000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2404@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexander Slastnikov (CEMI)\, Ernst Presman (CEMI RA
N)\n\nThe talk is devoted to the general one-dimensional diffusion. We dis
cuss the definition and characterization of such processes: scale\, speed
measure\, killing measure. The generating operator is considered on an ext
ended space of functions (as compared with a classical approach). We give
a local characterization potential functions and excessive functions. For
the general one-dimensional diffusion we give a necessary and sufficient c
onditions that the optimal strategy in the optimal stopping problem has a
threshold or an island character.\n\nhttps://indico.math.cnrs.fr/event/69
9/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:20150902T085000Z
DTEND:20150902T093000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2405@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ernst Eberlein (University of Freiburg)\n\nA brief i
ntroduction into the Lévy Libor and the Lévy forward process model is gi
ven. Basic properties of these two frameworks are discussed. The main goal
is to derive formulas for price sensitivities of standard fixed income de
rivatives. Two approaches are discussed. The first approach is based on th
e integration–by–parts formula\, which lies at the core of the applica
tion of the Malliavin calculus to finance. The second approach consists in
using Fourier based methods for pricing derivatives. We illustrate the re
sult by applying the formulas to a caplet price where the underlying model
is driven by a time–inhomogeneous Gamma process and alternatively by a
Variance Gamma process. A comparison between the two approaches which come
from totally different mathematical fields is made.\nThis is joint work w
ith M'hamed Eddahbi and Sidi Mohamed Lalaoui\n\nhttps://indico.math.cnrs.f
r/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:20150904T130000Z
DTEND:20150904T133000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2406@indico.math.cnrs.fr
DESCRIPTION:Speakers: Vadim Arkin (CEMI)\, Alexander Slastnikov (CEMI)\n\n
We describe a variational approach to solving optimal stopping problems fo
r diffusion processes. In the framework of this approach\, one can find op
timal stopping time over 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 gi
ve necessary and sufficient conditions for optimality of stopping time ove
r this class.\nFor one-dimensional diffusion processes and two families of
`semi-intervals’\, we set necessary and sufficient conditions under whi
ch the optimal stopping time has a threshold structure.\nWe study smooth p
asting condition from a variational view\, present some examples when the
solution to the free-boundary problem is not the solution to the optimal s
topping problem\, and give some results about a relation between solutions
to free-boundary problem and optimal stopping problem. At last\, some app
lications of these results to both investment timing and optimal abandonme
nt models are considered.\n\nhttps://indico.math.cnrs.fr/event/699/contrib
utions/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:20150904T092000Z
DTEND:20150904T095000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2407@indico.math.cnrs.fr
DESCRIPTION:Speakers: Peng Luo (University of Konstanz)\n\nWe consider mul
tidimensional quadratic BSDEs with generators which can be separated into
a coupled and an uncoupled part which allows to analyse the degree of coup
ling of the system in terms of the growth coefficients. We provide conditi
ons on the relationship between the size of the terminal condition and the
degree 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:20150902T120000Z
DTEND:20150902T124000Z
DTSTAMP:20230925T133400Z
UID:indico-contribution-2408@indico.math.cnrs.fr
DESCRIPTION:Speakers: Tahir Choulli (UNiversity of Alberta)\, Martin Schwe
izer (ETH Zurich)\n\nA classic result (due to Borwein and Lewis) in the th
eory of optimisation under constraints says the following. Suppose we have
n measurable functions a_i in L^q on a finite measure space and a nonnega
tive function x in L^p. Call b_i the integrals of x against a_i. Then ther
e exists a function z in the norm interior of L^infty which has the same i
ntegrals b_i against a_i as x. So if the constraints 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 with infinitely many\, measurably
parametrised constraints\, and we show how this comes up and can be used
in arbitrage theory.\n\nThis is based on joint work with Tahir Choulli (Un
iversity 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