Optimal switching under a regime-switching model with two-time-scale Markov chains
Speaker:Prof. Zhen WU
Vice Dean of Taishan College
Shandong University
Date & Time:2 Feb 2015 (Monday) 10:00 - 11:00
Venue:E11-1009
Organized by:Department of Mathematics

Abstract

In this talk, it is concerned with a probabilistic approach to an optimal switching problem. The dynamics of the system consists of a set of diffusions coupled by a finite-state Markov chain. It is shown that the value function and the optimal strategy can be given in terms of the solution of an oblique reflected backward stochastic differential equations (BSDEs) with Markov chain. The oblique reflected BSDEs also give a probabilistic interpretation for a system of variational inequalities.

In many applications, the underlying Markov chain exhibits two-time-scale structure. In this case, the value functions for the original problem is shown to converge to the value functions of a limit problem as the fluctuation rate shrinks to zero. The main advantage of this two-time-scale approach is the reduction of dimensionality. The limit problem is much easier to solve and its optimal switching solution leads to approximate solutions to the original problem. Finally, a numerical example is provided to demonstrate the convergence result.

Biography

Professor Zhen Wu received his MSc from Shandong University in 1994 and PhD from Shandong University in 1997. Since graduation, he has been working in computational and applied mathematics at Shandong University and University of Maine Le Mans (France). Now he is working as a Professor of Mathematics, Vice dean of School of Mathematics and Vice dean of Taishan College at Shandong University . Professor Wu’s research interests are: Stochastic optimal control, forward-backward stochastic differential equation, differential games, mathematical finance.