A mutual insurance diffusion stochastic control problem

This paper determines the optimal loading factor policy of a mutual insurance firm. Insurance is viewed as a collective process of N persons paying fixed (or variable, contingent) premiums and seeking protection against claims. Risk reduction for each person is then exercised through a distribution of risk by aggregating individual risks and by accumulating cash (net of operating expenses) to meet possible contingent claims. By assuming an approximate claims diffusion process, stochastic control problems for selecting the optimum loading factor policies are stated and resolved analytically. In particular, the implicit cost of bankruptcy is computed and an optimum variable-feedback loading policy is established.