OPTIMAL DYNAMIC EQUILIBRIUM IN INSURANCE POLICIES

Insurance companies sell contracts of various types each of them having a specific probability of return. Insurers may also own, at the same time, several insurance contracts which evolve through time. In this context, expectation and variance of the free reserves appear as functions of the number of customers in different classes as well as their evolution. Assuming that the customer system can be formulated as an open Markov one characterized by free entry, it is interesting to seek the optimal new customer distribution over the different customer classes j, which permits the minimization of the variance of free reserves for a desired average level of free reserves at a given time horizon. It is shown that, under some conditions, the customer system converges to an optimal growth steady state.