Tue, 12 Oct 2010
14:15 - 16:15
Time inconsistent stochastic control" (joint with Agatha Murgoci and Xunyu Zhou)
(Columbia University/Stockholm School of Economics)
"We present a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for subgame perfect Nash equilibrium points.
For a general controlled Markov process and a fairly general objective functional we derive an extension of the standard Hamilton-Jacobi-Bellman equation, in the form of a system of non-linear equations. We give some concrete examples, and in particular we study the case of mean variance optimal portfolios with wealth dependent risk aversion"