Prof.
Jean Jacod
(Université Pierre-et-Marie Curie)
11/30/15, 10:00 AM
We consider an Itô semimartingale which is observed along a discrete time grid, within a fixed
time interval. The observations are contaminated by noise, and the semimartingale has jumps with
a degree of activity bigger than 1. Our aim is to revisit the estimation of the integrated volatility in
such a setting: we use a mixture of the pre-averaging method (to eliminate noise) and of the...
Prof.
Ernst Eberlein
(University of Freiburg)
11/30/15, 11:00 AM
In classical economic theory the law of one price prevails and market participants trade
freely in both directions at the same price. This approach is appropriate for highly liquid
markets. In the absence of perfect liquidity, the law of one price has to be replaced by a
two price economy where market participants continue to trade freely with the market but
the terms of trade now depend...
Prof.
Nizar Touzi
(Ecole Polythecnique)
11/30/15, 11:50 AM
We consider a general 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 standard stochastic control problem, so that the principal's problem is solved by the standard tools of control theory. Our proofs rely on the Backward Stochastic Differential Equations approach to non-Markovian stochastic control,...
Prof.
Ljudmila Bordag
(University of Applied Sciences Zittau/Görlitz)
11/30/15, 2:30 PM
Management of a portfolio that includes an illiquid asset is an important
problem of modern mathematical finance. One of the ways to model illiquidity
among others is to build an optimization problem and assume that one of the
assets in a portfolio can not be sold until a certain finite, infinite or random
moment of time. This approach arises a certain amount of models that are
actively...
Prof.
Marina Kleptsyna
(Université du Maine)
11/30/15, 3:20 PM
We present a new approach to the analysis of mixed processes: for $t\in [0,T]$
$
\hspace{6cm} X_t = B_t + G_t,
$
where $B_t$ is a Brownian motion and $G_t$ is an independent centered
Gaussian process.
We obtain a new canonical innovation representation of $X$, using linear
filtering theory.
When the kernel
$
\hspace{5cm} K(s,t) = \frac{\partial^2}{\partial s\partial...
Prof.
Jordan Stoyanov
(Newcastle University & University of Ljubljana)
11/30/15, 4:20 PM
The talk is on selected new results on uniqueness and
non-uniqueness of distributions in terms of their moments.
The results cover distributions of random variables, random vectors and
stochastic processes, including solutions of SDEs. A couple of open
questions will be outlined.
Prof.
Loïc Chaumont
(Université d'Angers)
11/30/15, 5:00 PM
We show that any $\mathbb{R}^d$-valued self-similar Markov process $X$ with index $\alpha>0$ absorbed at
0, can be represented as a path transformation of some Markov additive process (MAP) $(\theta,\xi)$ in $S_{d-1}\times\mathbb{R}$.
This result extends the well known Lamperti transformation. Then we prove that the
same transformation of the dual MAP in the weak sense of $(\theta,\xi)$...
Prof.
Hans-Jürgen Engelbert
(Friedrich Schiller-University of Jena, Institute of Mathematics)
12/1/15, 10:00 AM
For many problems in the theory of stochastic processes and its applications it is of great importance to know effective
criteria ensuring that a given local martingale is a true martingale or even a uniformly integrable martingale. This question is closely related to absolute continuity of probability measures and change of measure and has been the subject of research over many decades....
Prof.
Martin Schweizer
(ETH Zurich)
12/1/15, 11:00 AM
We discuss a systematic approach to the valuation of general European contingent claims in general continuous-time financial markets. We want to provide bounds on economically reasonable valuations that do not depend too much on precise assumptions on the underlying primary assets. This allows us to provide a general result on put-call parity and to give an explanation for some pricing...
Prof.
Yuri Kabanov
(Université Franche-Comté)
12/1/15, 11:50 AM
The Cherny-Shiryaev criterion provides a description of predictable processes which are integrable with
respect to a vector-valued semimartingale in terms of its local characteristics.
We provide an example how this result can be used in the problem of existence of local martingale numéraire
in a model of financial market which has no asymptotic arbitrage opportunities of the first kind.
Prof.
Anis Matoussi
(Université du Maine)
12/1/15, 2:30 PM
We present an overview on different classes of nonlinear stochastic partial differential equations (SPDEs in short). In particular, we focus on providing a probabilistic representation of solution of Fully nonlinear SPDEs (stochastic Viscosity solutions) by means of solution of the associated class of Second order BSDEs. This presentation includes the numerical study of quasilinear and...
Prof.
Said Hamadène
(Université du Maine)
12/1/15, 3:20 PM
In this talk, we discuss a new existence and uniqueness result of a continuous viscosity solution for integro-partial differential equation (IPDE in short).
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...
Prof.
Lioudmila Vostrikova
(Université d'Angers)
12/1/15, 4:20 PM
We study the exponential functionals of
the processes with independent increments which are integrable semi-martingales with
absolutely continuous characteristics. We give necessary and sufficient conditions for existence of Laplace exponent, and also the
sufficient conditions of finiteness of the moments of exponential functionals. We derive
a recurrent integral equation for its Mellin...
