Insurance Pricing and Regulation under Uncertainty: A Chance-Constrained Approach

Abstract

A financial model of the non-life insurer under uncertainty is developed. The model recognizes the stochastic nature of both the insurer's underwriting and investment income. The total risk faced by the insurer, which includes both underwriting and investment risk, is considered. The impact of regulatory constraints on the insurer's profits also is analyzed. Moreover, the costs of regulation imposed on the insurer are assessed in a non-linear, chance-constrained, programming framework. In general, the model shows that economic tradeoffs must be considered when management or regulatory decisions are made because of the numerous interrelationships among variables in the model and in the real world. A simplified financial model of a non-life insurer's behavior under uncertainty is developed in this paper. It is an extension of an earlier paper by the authors (24) that examined insurer behavior under the simplified conditions of partial certainty where the assumption was that the insurer could accurately forecast its underwriting and investment results. In this paper, the stochastic nature of the insurer's underwriting and investment income is considered which greatly complicates the model, but makes it considerably more realistic.