Optimal switching problems under partial information

Abstract

AbstractIn this paper, we formulate and study an optimal switching problem under partial information. In our model, the agent/manager/investor attempts to maximize the expected reward by switching between different states/investments. However, he is not fully aware of his environment and only an observation process, which contains partial information about the environment/underlying, is accessible. It is based on the partial information carried by this observation process that all decisions must be made. We propose a probabilistic numerical algorithm, based on dynamic programming, regression Monte Carlo methods, and stochastic filtering theory, to compute the value function. In this paper, the approximation of the value function and the corresponding convergence result are obtained when the underlying and observation processes satisfy the linear Kalman–Bucy setting. A numerical example is included to show some specific features of partial information.