Campuses:

Stochastic differential games

Friday, May 11, 2018 - 9:00am - 9:50am
Tyrone Duncan (University of Kansas)
Stochastic differential games have been used as models for a wide variety of physical systems. These games are a natural evolution from some stochastic control problems. Two well known methods to find optimal control strategies for a stochastic differential game are solving Hamilton-Jacobi-Isaacs equations which are nonlinear partial differential equations or solving backward stochastic differential equations. Both of these approaches are often difficult to solve for explicit optimal control strategies.
Thursday, May 10, 2018 - 11:00am - 11:50am
Nicolai Krylov (University of Minnesota, Twin Cities)
We show that the value function in a stochastic differential game does not change if we keep the same space $(\Omega,\cF)$ but introduce probability measures by means of Girsanov's transformation {\em depending\/} on the policies of the players. We also show that the value function does not change if we allow the driving Wiener processes to depend on the policies of the players. Finally, we show that the value function does not change if we perform a random time change with the rate depending on the policies of the players.
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