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BEGIN:VEVENT
SUMMARY:Estimation of volatility in presence of high activity jumps\, nois
e and irregular sampling
DTSTART;VALUE=DATE-TIME:20151130T090000Z
DTEND;VALUE=DATE-TIME:20151130T094000Z
DTSTAMP;VALUE=DATE-TIME:20210516T220322Z
UID:indico-contribution-866-2726@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jean Jacod (Université Pierre-et-Marie Curie)\nWe c
onsider an Itô semimartingale which is observed along a discrete time gri
d\, within a fixed\ntime interval. The observations are contaminated by no
ise\, and the semimartingale has jumps with\na degree of activity bigger t
han 1. Our aim is to revisit the estimation of the integrated volatility i
n\nsuch a setting: we use a mixture of the pre-averaging method (to elimin
ate noise) and of the empirical\ncharacteristic function method\, which ha
s been shown to be efficient (after proper de-biasing) even\nwhen the jump
activity is bigger than 1\, in contrast with most other methods.\n\n\nThi
s is a joint work with Viktor Todorov.\n\nhttps://indico.math.cnrs.fr/even
t/866/contributions/2726/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/866/contributions/2726/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valuation\, put-call parity and bubbles
DTSTART;VALUE=DATE-TIME:20151201T100000Z
DTEND;VALUE=DATE-TIME:20151201T104000Z
DTSTAMP;VALUE=DATE-TIME:20210516T220322Z
UID:indico-contribution-866-2727@indico.math.cnrs.fr
DESCRIPTION:Speakers: Martin Schweizer (ETH Zurich)\nWe discuss a systemat
ic approach to the valuation of general European contingent claims in gene
ral continuous-time financial markets. We want to provide bounds on econom
ically reasonable valuations that do not depend too much on precise assump
tions on the underlying primary assets. This allows us to provide a genera
l result on put-call parity and to give an explanation for some pricing an
omalies observed in the literature.\nThis is based on joint work with Mart
in Herdegen (ETH Zurich).\n\nhttps://indico.math.cnrs.fr/event/866/contrib
utions/2727/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/866/contributions/2727/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inversion\, duality and h-processes of self-similar Markov process
es
DTSTART;VALUE=DATE-TIME:20151130T160000Z
DTEND;VALUE=DATE-TIME:20151130T164000Z
DTSTAMP;VALUE=DATE-TIME:20210516T220322Z
UID:indico-contribution-866-2728@indico.math.cnrs.fr
DESCRIPTION:Speakers: Loïc Chaumont (Université d'Angers)\nWe show that
any $\\mathbb{R}^d$-valued self-similar Markov process $X$ with index $\\a
lpha>0$ absorbed at \n0\, can be represented as a path transformation of s
ome Markov additive process (MAP) $(\\theta\,\\xi)$ in $S_{d-1}\\times\\ma
thbb{R}$. \nThis result extends the well known Lamperti transformation. Th
en we prove that the \nsame transformation of the dual MAP in the weak sen
se of $(\\theta\,\\xi)$ is itself in weak duality with $X$\, with respect
to the \nmeasure $\\pi(x/\\|x\\|)\\|x\\|^{\\alpha-d}dx$\, if and only if $
(\\theta\,\\xi)$ is reversible with respect to the measure $\\pi(s)ds$\, w
here $ds$ is\nthe Lebesgue measure on $S_{d-1}$. Besides\, the dual proce
ss $\\widehat{X}$ has the same law as the inversion \n$(X_{\\gamma_t}/\\|
X_{\\gamma_t}\\|^2\,t\\ge0)$ of $X$\, where $\\gamma_t$ is the inverse of
$t\\mapsto\\int_0^t\\|X\\|_s^{-2\\alpha}\\\,ds$. \nAs an application\, we
prove that in some instances\, the Kelvin transform of $X$ can be obtaine
d as an $h$-transform of some functional of $X$.\n\nThis is a joint work w
ith Larbi Alili\, Piotr Graczyk and Tomasz Zak.\n\n$~\\\\~\\\\~\\\\~\\\\~\
\\\~\\\\$\n\nhttps://indico.math.cnrs.fr/event/866/contributions/2728/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/866/contributions/2728/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On exponential functionals for processes with independent incremen
ts
DTSTART;VALUE=DATE-TIME:20151201T152000Z
DTEND;VALUE=DATE-TIME:20151201T160000Z
DTSTAMP;VALUE=DATE-TIME:20210516T220322Z
UID:indico-contribution-866-2729@indico.math.cnrs.fr
DESCRIPTION:Speakers: Lioudmila Vostrikova (Université d'Angers)\nWe stud
y the exponential functionals of\nthe processes with independent incremen
ts which are integrable semi-martingales with\nabsolutely continuous chara
cteristics. We give necessary and sufficient conditions for existence of L
aplace exponent\, and also the\nsufficient conditions of finiteness of the
moments of exponential functionals. We derive\na recurrent integral equat
ion for its Mellin transform and recurrent\nformulas for the moments. In
particular\, we obtain the results for Levy subordinators given in the pap
er of Bertoin\, Yor (2005).\n\n\n\nThis is joint work with Paavo Salminen
(Turku University\, Finland).\n\nhttps://indico.math.cnrs.fr/event/866/con
tributions/2729/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/866/contributions/2729/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Two price valuation theory
DTSTART;VALUE=DATE-TIME:20151130T100000Z
DTEND;VALUE=DATE-TIME:20151130T104000Z
DTSTAMP;VALUE=DATE-TIME:20210516T220322Z
UID:indico-contribution-866-2730@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ernst Eberlein (University of Freiburg)\nIn classica
l economic theory the law of one price prevails and market participants tr
ade\nfreely in both directions at the same price. This approach is appropr
iate for highly liquid\nmarkets. In the absence of perfect liquidity\, the
law of one price has to be replaced by a\ntwo price economy where market
participants continue to trade freely with the market but\nthe terms of tr
ade now depend on the direction of the trade.\nWe give an introduction to
this new approach. The two prices are termed bid and ask or\nlower and upp
er price but they should not be confused with the literature relating bid-
ask\nspreads to transaction costs or other frictions involved in modeling
financial markets. The\ntwo prices are determined in a non marketclearing
equilibrium with a view to make loss\nexposures acceptable. Acceptability
is defined via a positive expectation under a family of\ntest measures or
scenarios. As a result the bid price is the infimum of test valuations whe
reas\nthe ask price is the supremum of such valuations. The two prices are
related to nonlinear\nexpectation operators. We consider examples where t
he uncertainty is given by purely\ndiscontinuous Lévy processes. Various
aspects such as liquidity measurement and portfolio\ntheory are discussed.
Finally we present a defaultable asset price model (DAM) in the\ncontext
of the two price valuation. $\\hspace{70cm}$\n\nhttps://indico.math.cnrs.f
r/event/866/contributions/2730/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/866/contributions/2730/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Optimization problem for a portfolio with an illiquid asset: Lie g
roup analysis
DTSTART;VALUE=DATE-TIME:20151130T133000Z
DTEND;VALUE=DATE-TIME:20151130T141000Z
DTSTAMP;VALUE=DATE-TIME:20210516T220322Z
UID:indico-contribution-866-2731@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ljudmila Bordag (University of Applied Sciences Zitt
au/Görlitz)\nManagement of a portfolio that includes an illiquid asset is
an important\nproblem of modern mathematical finance. One of the ways to
model illiquidity\namong others is to build an optimization problem and as
sume that one of the\nassets in a portfolio can not be sold until a certai
n finite\, infinite or random\nmoment of time. This approach arises a cert
ain amount of models that are\nactively studied at the moment.\nWorking in
the Merton’s optimal consumption framework with continuous\ntime we con
sider an optimization problem for a portfolio with an illiquid\, a\nrisky
and a risk-free asset. Our goal in this paper is to carry out a complete\n
Lie group analysis of PDEs describing value function and investment and co
nsumption strategies for an portfolio with an illiquid asset that is sold
in a random moment of time with a prescribed liquidation time distribution
. Study of\noptimization problems with an illiquid asset leads to three di
mensional non-\nlinear Hamilton-Jacobi-Bellman (HJB) equations. Such equat
ions are not only\ntedious for analytical methods but are also quite chall
enging form a numeric\npoint of view. To reduce the three-dimensional prob
lem to a two-dimensional\none or even to an ODE one uses some substitution
s\, yet the methods used to\nfind such substitutions are rarely discussed
by the authors.\nWe find the admitted Lie algebra for a certain class of l
iquidation time distributions in cases of HARA and log utility functions a
nd formulated theorems\nfor these cases. We use them to obtain correspondi
ng reductions. Several of\nthese substitutions were used in other papers b
efore and other ones are new to\nour knowledge. This method gives us the p
ossibility to provide a complete set\nof non-equivalent substitutions and
reduced equations.\n\nhttps://indico.math.cnrs.fr/event/866/contributions/
2731/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/866/contributions/2731/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Probabilistic interpretation for Fully nonlinear Stochastic PDEs
DTSTART;VALUE=DATE-TIME:20151201T133000Z
DTEND;VALUE=DATE-TIME:20151201T141000Z
DTSTAMP;VALUE=DATE-TIME:20210516T220322Z
UID:indico-contribution-866-2732@indico.math.cnrs.fr
DESCRIPTION:Speakers: Anis Matoussi (Université du Maine)\nWe present an
overview on different classes of nonlinear stochastic partial differential
equations (SPDEs in short). In particular\, we focus on providing a proba
bilistic representation of solution of Fully nonlinear SPDEs (stochastic
Viscosity solutions) by means of solution of the associated class of Seco
nd order BSDEs. This presentation includes the numerical study of quasilin
ear and semilinear SPDEs (the time discretization error and numerical tes
ts) and some applications in pathwise stochastic control problems arising
in finance.\n\n$~\\\\~\\\\~\\\\~\\\\~\\\\$\n\nhttps://indico.math.cnrs.fr
/event/866/contributions/2732/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/866/contributions/2732/
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:20151201T142000Z
DTEND;VALUE=DATE-TIME:20151201T150000Z
DTSTAMP;VALUE=DATE-TIME:20210516T220322Z
UID:indico-contribution-866-2733@indico.math.cnrs.fr
DESCRIPTION:Speakers: Said Hamadène (Université du Maine)\nIn this talk\
, we discuss a new existence and uniqueness result of a continuous viscosi
ty solution for integro-partial differential equation (IPDE 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 solutio
n of equation with a non local term. Our method is based on the link of th
ose IPDEs with backward stochastic differential equations (BSDEs in short)
with jumps for which we already know that the solution exists and is uniq
ue.\n\nReferences:\n\n- [1] Alvarez\, O.\, Tourin\, A. Viscosity solutions
of nonlinear integro-differential equations\, *Annales de l’Institut\nH
enri Poincaré. Analyse non linéaire\, Elsevier 13(3)\, pp. 293-317\, 199
6.*\n- [2] Barles\, G.\, Buckdahn R and Pardoux E.\, Backward stochastic d
ifferential equations and integral-partial differential equations\, *Stoch
astics: An International Journal of Probability and Stochastic Processes\,
60\, 57\n83\, 1997.*\n- [3] Barles\, G. and Imbert\, C.\, Second-Order El
liptic Integro-Differential Equations : Viscosity Solutions' Theory\nRevis
ited\, *Ann. Inst. H. Poincaré- Anal. Non Linéaire 25(3): 567-585\, 2008
.*\n- [4] Dumetrescu R.\, Quenez M.-C.\, Sulem A.\, Reflected BSDEs with j
umps and partial integro-differential varia-\ntional inequalities\, *Resea
rch Report No 8213\, Project-Teams Mathrisk (2013).*\n- [5] Hamadène S.\,
Ouknine Y.\, Reflected backward stochastic differential equation with jum
ps and random obstacle\, *Electron. J. Probab.\, 8: 2 - 20\, 2003.*\n- [6]
Harraj N.\, Ouknine Y. and Turpin I.\, Double barriers Reflected BSDEs wi
th jumps and viscosity solutions of\nparabolic Integro-differential PDEs\,
*Journal of Applied Mathematics and Stochastic Analysis\, 1: 37-53\, 2005
.*\n- [7] Tang\, S.J. and Li\, X.J.\, Necessary conditions for optimal con
trol of stochastic systems with random jumps\,\n*SIAM J. Control Optim. 32
: 14471475\, 1994.*\n\nhttps://indico.math.cnrs.fr/event/866/contributions
/2733/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/866/contributions/2733/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On one application of the Cherny-Shiryaev criterion of stochastic
integrability
DTSTART;VALUE=DATE-TIME:20151201T105000Z
DTEND;VALUE=DATE-TIME:20151201T113000Z
DTSTAMP;VALUE=DATE-TIME:20210516T220322Z
UID:indico-contribution-866-2734@indico.math.cnrs.fr
DESCRIPTION:Speakers: Yuri Kabanov (Université Franche-Comté)\nThe Chern
y-Shiryaev criterion provides a description of predictable processes whic
h are integrable with\nrespect to a vector-valued semimartingale in terms
of its local characteristics. \nWe provide an example how this result can
be used in the problem of existence of local martingale numéraire\nin a m
odel of financial market which has no asymptotic arbitrage opportunities
of the first kind.\n\nhttps://indico.math.cnrs.fr/event/866/contributions/
2734/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/866/contributions/2734/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Martingale Property of Local Martingales: When a Local Mart
ingale is a True Martingale?
DTSTART;VALUE=DATE-TIME:20151201T090000Z
DTEND;VALUE=DATE-TIME:20151201T094000Z
DTSTAMP;VALUE=DATE-TIME:20210516T220322Z
UID:indico-contribution-866-2735@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hans-Jürgen Engelbert (Friedrich Schiller-Universit
y of Jena\, Institute of Mathematics)\nFor many problems in the theory of
stochastic processes and its applications it is of great importance to kno
w effective\ncriteria ensuring that a given local martingale is a true mar
tingale or even a uniformly integrable martingale. This question is closel
y related to absolute continuity of probability measures and change of mea
sure and has been the subject of research over many decades. Starting from
an arbitrary nonnegative local martingale\, the aim of the present talk i
s to give necessary and sufficient conditions in terms of another but intr
insic probability which is locally equivalent to the given one. The result
s and the verifiability of the conditions will be illustrated by several a
pplications. First we shall consider a geometric Ornstein-Uhlenbeck financ
ial market. Then we pass on to general stochastic exponentials of continuo
us local martingales and it will be demonstrated that Novikov’s and Kaza
maki’s conditions are simple consequences of ours. Special examples are
discussed for stochastic exponentials of solutions\nof one-dimensional SDE
s without drift in which case purely analytical criteria in terms of the d
iffusion coefficient are obtained. In particular\, if these criteria are n
ot satisfied\, then the corresponding process is a strict local martingale
which is also referred to as a bubble in the mathematical finance literat
ure.\n\n$~\\\\~\\\\~\\\\~\\\\~\\\\~\\\\~\\\\~\\\\$\n\nhttps://indico.math.
cnrs.fr/event/866/contributions/2735/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/866/contributions/2735/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mixed Gaussian processes: a filtering approach
DTSTART;VALUE=DATE-TIME:20151130T142000Z
DTEND;VALUE=DATE-TIME:20151130T150000Z
DTSTAMP;VALUE=DATE-TIME:20210516T220322Z
UID:indico-contribution-866-2736@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marina Kleptsyna (Université du Maine)\nWe present
a new approach to the analysis of mixed processes: for $t\\in [0\,T]$\n\n
$\n \\hspace{6cm} X_t = B_t + G_t\,\n$\n\nwhere $B_t$ is a Brownian
motion and $G_t$ is an independent centered\nGaussian process.\nWe obtain
a new canonical innovation representation of $X$\, using linear\nfiltering
theory.\n\nWhen the kernel\n\n$\n \\hspace{5cm} K(s\,t) = \\frac{\\partia
l^2}{\\partial s\\partial t} E G_t G_s\,\\quad s\\ne t\n$\n\nhas a weak s
ingularity on the diagonal\, our results generalize the\nclassical innovat
ion formulas beyond the square integrable setting.\nFor kernels with stron
ger singularity\, our approach is applicable to\nprocesses with additional
``fractional'' structure\,\nincluding the mixed fractional Brownian motio
n from mathematical finance.\nWe show how previously known measure equival
ence relations and\nsemimartingale properties follow from our canonical\nr
epresentation in a unified way\, and complement them with new formulas for
\nRadon-Nikodym densities.\n\nhttps://indico.math.cnrs.fr/event/866/contri
butions/2736/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/866/contributions/2736/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moral hazard and second order backward SDEs
DTSTART;VALUE=DATE-TIME:20151130T105000Z
DTEND;VALUE=DATE-TIME:20151130T113000Z
DTSTAMP;VALUE=DATE-TIME:20210516T220322Z
UID:indico-contribution-866-2737@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nizar Touzi (Ecole Polythecnique)\nWe consider a gen
eral formulation of the Principal-Agent problem with a lump-sum payment on
a finite horizon. Our main result is a reduction of this problem to a sta
ndard stochastic control problem\, so that the principal's problem is solv
ed by the standard tools of control theory. Our proofs rely on the Backwar
d Stochastic Differential Equations approach to non-Markovian stochastic
control\, and more specifically\, on the recent extensions to the second o
rder case.\n\nhttps://indico.math.cnrs.fr/event/866/contributions/2737/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/866/contributions/2737/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Probability Distributions: Characterizations by Their Moments
DTSTART;VALUE=DATE-TIME:20151130T152000Z
DTEND;VALUE=DATE-TIME:20151130T155000Z
DTSTAMP;VALUE=DATE-TIME:20210516T220322Z
UID:indico-contribution-866-2738@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jordan Stoyanov (Newcastle University & University o
f Ljubljana)\nThe talk is on selected new results on uniqueness and\nnon-u
niqueness of distributions in terms of their moments.\nThe results cover d
istributions of random variables\, random vectors and\nstochastic processe
s\, including solutions of SDEs. A couple of open\nquestions will be outli
ned.\n\nhttps://indico.math.cnrs.fr/event/866/contributions/2738/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/866/contributions/2738/
END:VEVENT
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