Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)
Non-zero-sum Stochastic Differential Games of Control and Stopping
Tuesday, April 27, 2010 at 01:45pm - 02:45pm
Speaker: Qinghua Li, Columbia University
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)
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)
Location Hill 525