Setting the optimal limit value of motor insurance coverage by stochastic optimization

Abstract

In this paper, we provide an alternative to a passive approach to the selection of insurance products or policy con-ditions. Specifically, we propose a method to make a decision about the optimal limit value for motor insurance coverage. Respecting the stochastic nature of individual loss, we formulate a problem of stochastic programming in which the total potential financial loss of the policyholder is minimized. Actually, we present a general optimization problem in which various relevant probability distributions of individual loss may be considered. In addition, we extend the work of Valecký (2017) and derive an insurance rate that describes better the dependence between the pure premium and the given limit value under the assumption that the individual potential loss follows a gamma distribution. Because of the absence of a closed-form solution, sample average approximation is applied to the objective function and the optimal solution to this approximated (SAA) problem is determined. Finally, the quality of the obtained solution is assessed by approximation to the optimality gap representing the difference between our candidate and the true solution.