Bernt Øksendal's 60th Anniversary

CMA, University of Oslo, Norway
June 9-10, 2005.

Collection of Abstracts (alphabetically ordered):

FRANCESCA BIAGINI, University of Bologna, Italy
Title: Utility optimization problems and minimal hedging for insiders
Abstract: See separate .pdf-file

KJELL ARNE BREKKE, The Ragnar Frisch Centre for Economic Research, University of Oslo, Norway
Title: Using stochastic control to understand ecosystems with humans.
Abstract: tba

SANDY DAVIE, University of Edinburgh, Scotland
Title: Pointwise limits of analytic functions.
Abstract: This talk attempts to answer the following question: given a complex-valued function on an open set in the complex plane when can we express it as the pointwise limit of a sequence of analytic functions? Extensions to several complex variables will also be considered.

YAOZHONG HU, University of Kansas, USA
Title: Detecting moving objects under ocean
Abstract: This is an ongoing project with Mike Kouritzin. The objects under ocean emits sound. The sound is received with some white noise corruption. The objective is to use nonlinear filtering theory to detect how many moving objects and their position and speed etc.

YURI KONDRATIEV, University of Bielefeld, Germany
Title: Interacting particle systems in continuum: from stochastic dynamics to hydrodynamics.
Abstract: We will discuss some recent developments in the stochastic dynamics theory for interacting particle systems in continuum. Constructions of non-equilibrium stochastic dynamics for some classes of Markov processes on configuration spaces will be presented. Our main attention is devoted to such cases as birth-and-death and hopping particles processes in continuum. As applications of decribed results we study the hydrodynamic scaling limit for some infinite particle stochastic dynamics.

EDWARD LUNGU, University of Botswana, Gaborone, Botswana
Title: Application of Lie Symmetries to Determine an Optimal Investment Policy.
Abstract: See separate .pdf-file

HABIB OUERDIANE, University of Tunis El Manar Tunisia
Title: Solutions of stochastic heat equations of convolution type.
Abstract: See separate .pdf-file

JURGEN POTTHOFF, University of Mannheim, Germany
Title: Sample Properties of Random Fields.
Abstract: The talk will focus on results about the existence of modifications of a random field, which are sample continuous or sample differentiable. In the case of continuity, the underlying index space of the random field is a metric space admitting a certain separability condition (stronger than usual separability), and a generalized version of the Kolmogorov-Chentsov-argument for this situation will be presented. Examples of such metric spaces are the open subsets of the m-dimensional euclidean space. Sample differentiablity will be discussed for random fields indexed by an open, pathwise connected subset of the m-dimensional euclidean space. If time allows, also criteria for whether a random field indexed by a separable metric space has a modification which is separable or measurable will be given.

NICOLAS PRIVAULT, Université de La Rochelle, France
Title: An extension of Clark's formula in distribution sense with a derivation operator on Poisson space
Abstract: The Clark formula on Poisson space has been extended in the sense of white noise distributions and applied to hedging in a market with jumps by Aase et al., Finance Stoch. 4 (2000). However the operator used in this work is a finite difference operator and as such it lacks the derivation property which can be useful in a number of applications. In this talk we would like to present a different extension of the Clark formula using a gradient operator having the derivation property.

MARTA SANZ-SOLÉ, University of Barcelona, Spain
Title: Large deviation estimates for rough paths of fractional Brownian motion.
Abstract: See separate .pdf-file

LUDWIG STREIT, University of Bielefeld, Germany and University of Madeira, Portugal
Title: Stochastic Optimal Control: A Simple Example.
Abstract: (Preliminary) We discuss a class of examples for which the dynamic programming equation is exactly soluble.

AGNES SULEM, INRIA, France
(joint work with A. Kohatsu-Higa (INRIA))
Title: Utility maximization in an insider influenced market.
Abstract: We study a controlled stochastic system whose state is described by a stochastic differential equation with anticipating coefficients. This setting is used to model markets where insiders have some influence on the dynamics of prices. We give a characterization theorem for the optimal logarithmic portfolio of an investor with a different information flow from that of the insider. We provide explicit results in the partial information case which we extend in order to incorporate the enlargement of filtration techniques for markets with insiders. Then, we consider a market with an insider who influences the drift of the underlying price asset process. We obtain some generalizations of insider modelling which may not be tractable by enlargement of filtration techniques.

ALI SULEYMAN USTUNEL, Ecole Nat. Sup. Telecomm. Paris, France
Title: Monge-Kantorovitch measure transportation on the Wiener space and its applications.
Abstract: We will give a brief account of the recent research on the problem of Monge-Kantorovitch on the Wiener space with the Wiener measure as well as with other general measures. Then we shall give a new application to the signal processing.

TUSHENG ZHANG, University of Manchester, England
Title: Perturbations of symmetric Markov processes.
Abstract: In this talk, I will report results on Girsanov transformation and Feynman-Kac formula for arbitrary symmetric Markov processes. The theory of Dirichlet forms will play an important role in the talk.