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In this paper, we study the optimization problem confronted by an insurance firm whose management can control its cash-balance dynamics by adjusting the underlying premium rate. The firm’s objective is to minimize the total deviation of its cash-balance process to some pre-set target levels by selecting an appropriate premium policy. We study the problem in a general framework assuming the state process is governed by a stochastic delay differential equation and the classical utility function being replaced by a recursive utility or stochastic differential utility (SDU). We derive a sufficient maximum principle for an optimal control of such a system and apply the result to discuss some optimal premium rate control problems.

Optimal premium policy of an insurance firm with delay and stochastic interest rate