We take two approaches, martingale techniques and BSDE’s, to solve non-zero-sum stochastic differential games in which all players can control and stop the games. Existence or non-existence of equilibrium stopping rules is proved under different conditions.
The martingale part provides equivalent martingale characterizations of Nash equilibrium strategies and of equilibrium stopping rules. When using equilibrium stopping rules, Isaac’s 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 BSDE’s. 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.
Speaker: Qinghua Li, Columbia University
Slides: (TBA)
Event Details
Non-zero-sum Stochastic Differential Games of Control and Stopping
- Event Date: April 27, 2010
- Event End Date: April 27, 2010
- Event Start Time: 1:45 PM
- Event End Time: 2:45 PM
- Event Location: Hill 525
- Event Type: Mathematical Finance and Probability Seminars
- Extra Info: Speaker: Qinghua Li, Columbia University