Andi Bodnariu: Stochastic differential games and time-inconsistent problems.

Abstract

In this licentiate presentation we consider stochastic games and game theoretic approaches to problems regarding optimal stochastic control and optimal stopping. This presentation consists of two parts corresponding to two papers.

The first part considers a game theoretic approach to a time-inconsistent stopping problem, where the time-inconsistency is due to non-exponential discounting. We introduce a new class of mixed stopping times and prove a verification result for an intra-personal equilibrium regarding this class of strategies. Furthermore we provide an example, where an equilibrium in this new class of mixed strategies is obtained.

The second part considers a controller stopper game with incomplete information. This can be seen as a game between owner and a manager of an asset. The manager can be either be effective or non-effective. An effective manager earns a salary paid by the owner and can increase the drift of the asset at a cost, while a non-effective cannot act. The owner cannot observe whether the manager is effective but can stop the game at any time. We derive a Nash equilibrium to this game, where the corresponding control and stopping time depend on a stochastic filtering process which corresponds to the conditional probability of the manager being active.