  In 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.
