# equilibrium strategy

Tuesday, May 8, 2018 - 11:00am - 11:50am

Jiongmin Yong (University of Central Florida)

Classical optimal control problems for (ordinary, stochastic, or evolutionary partial) differential equations have the following feature: When an optimal control is found for a given initial time and initial state, the optimal control will remain optimal as time goes by along the optimal trajectory. This is called the time-consistency of the problem. However, in reality, more than often, the optimal control will hardly stay optimal later on. This is called the time-inconsistency.

Tuesday, May 8, 2018 - 4:00pm - 4:30pm

Hongwei Mei (University of Kansas)

We consider an optimal control problem for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is time-inconsistent in general. Therefore, instead of finding a global optimal control (which is not possible), we look for a time-consistent (approximately) locally optimal equilibrium strategy.