Financial/Actuarial Mathematics Seminar

April 2, 2010



Non-zero-sum Stochastic Differential Games of Control and Stopping.

Qinghua Li

Department of Statistics, Columbia University

April 2, 2010



Abstract

We take two approaches, martingale techniques and BSDEÕs, to solve non-zero-sum stochastic differential games in which all players can control and stop the reward streams. The martingale part provides equivalent martingale characterizations of Nash equilibrium strategies and of equilibrium stopping rules. When using equilibrium stopping rules, IsaacÕs condition is necessary and sufficient for the existence of an equilibrium control set. The BSDE part identifies value processes of the games with solutions to backward SDEÕs. A multidimensional reflective BSDE is examined in two cases: Lipschitz growth only, and linear growth in the Markovian framework. An on-going project is to modify the non-zero-sum games in question to describe a stock market sensitive to several large traders.


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