A Stochastic Demand Model for Optimal Pricing of Non-Life Insurance Policies

A model for non-life insurance pricing is developed which is a stochastic version of that given in [4]. Two forms of stochasticity are considered: the uncertainty in the future market average premium and the uncertainty in the change of exposure from a given relative premium level. The optimal premium strategy is determined using dynamic programming, and this is compared with the deterministic model both analytically and numerically. If the market average premium is stochastic then the optimization problem reduces to a set of characteristic strip equations, which are analyzed using the phase diagram. If the change in exposure is stochastic then an analytical expression is found for the optimal premium strategy when the objective is to maximize the expected terminal wealth in an infinite insurance market with an exponential utility function. As the volatility is increased the optimal strategy changes to the breakeven premium strategy for both forms of stochasticity and positive risk aversion. However, the terminal optimal premium is given by the deterministic problem if the market average premium is stochastic.