A Malliavin Calculus Approach to General Stochastic Differential Games with Partial Information
In this article, we consider stochastic differential game where the state process is governed by a controlled Itô–Lévy process and the information available to the controllers is possibly less than the general information. All the system coefficients and the objective performance functional are assumed to be random. We use Malliavin calculus to derive a maximum principle for the optimal control of such problem. The results are applied to solve a worst-case scenario portfolio problem in finance.
KeywordsMalliavin calculus Stochastic differential game Stochastic control, Jump diffusion Partial information Optimal worst-case scenario portfolio
The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013)/ ERC grant agreement no .