Stochastic differential games: Occupation measure based approach

Stochastic Differential Portfolio Games

We study stochastic dynamic investment games in continuous time between two investors (players) who have available two different, but possibly correlated, investment opportunities. There is a single payoff function which depends on both investors’ wealth processes. One player chooses a dynamic portfolio strategy in order to maximize this expected payoff while his opponent is simultaneously choo...

Fuzzy differential games for nonlinear stochastic systems: suboptimal approach

A fuzzy differential game theory is proposed to solve the -person (or -player) nonlinear differential noncooperative game and cooperative game (team) problems, which are not easily tackled by the conventional methods. In this paper, both noncooperative and cooperative quadratic differential games are considered. First, the nonlinear stochastic system is approximated by a fuzzy model. Based on t...

Martingale Approach to Stochastic Differential Games of Control and Stopping

We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate conditions, we show that the game has a value and construct a saddle pair of optimal control and stopping strategies. Crucial in this construction is a characte...

Pathwise strategies for stochastic differential games with an erratum to ''Stochastic Differential Games with Asymmetric Information''

We introduce a new notion of pathwise strategies for stochastic differential games. This allows us to give a correct meaning to some statement asserted in [2].

Numerical Methods for Stochastic Differential Games