Uncertainty and inside information

Abstract

In this paper, we study a robust-entropic optimal control problem in the presence of inside information. To be more precise, we consider an economic agent who is allowed to invest her wealth in a classical Black-Scholes type financial market. From the beginning of the trading interval, the agent exclusively possesses some inside information concerning the future realization of the stock price process. However, we assume that she is uncertain as to the validity of this information, thus introducing in this way robust aspects to our model. The aim of the economic agent is to solve an expected utility maximization problem under the worst-case scenario, taking into account her enlarged information set. By formulating this problem as a two-player, zero sum stochastic differential game, we are able to provide closed form solutions for the optimal robust strategies and the robust value function, in the case of the exponential and the power utility functions.