Risk sensitive control and an optimal reinsurance model of a network of insurance companies

In this paper, we consider an optimal reinsurance problem of a network of homogeneous insurance companies. The problem is formulated as a risk sensitive control problem with small noise. We study the risk sensitive cost until the first exit time of the state process from a certain region. The limiting behavior of the risk sensitive problem is analyzed by presenting a corresponding differential game and an asymptotically optimal reinsurance policy is obtained by solving the differential game.