Finance Department


Date of this Version


Document Type



Journal of Actuarial Practice 7 (1999), pp. 205-222


Copyright 1999 Absalom Press


A simple stochastic model of an insurer's underwriting and related investment operations is used to determine the optimal amounts of written premiums for one period for the insurer's book of business. The written premium for each class is determined by the solution of a constrained optimization problem. The insurer's objective function is the expected profit on a book of business over the period. The insurer has a safety constraint where a certain portion of capital and surplus can be depleted with a small probability. This paper provides an explicit solution for optimum expected profit and corresponding written premiums by classes. Due to the closed form nature of the solution for expected profit, insights are given as to how the optimum expected profit depends upon the model's parameters.