Pricing of General Insurance with Optimal Control Theory.

Abstract

Generally, premium calculations are essential in the discussion of insurance products, such as expected value principles, higher order moments, and utility theory. However, all of these principles fail to account for the competitive nature of insurance pricing. Furthermore, Taylor (1986) formulates this problem as a model based on a demand law and distribution of claims. He uses a simple discrete time deterministic model, which is analyzed using pontryagin’s maximum principle to maximize the final wealth of an insurer. This leads to a bang-bang optimal premium strategy, which cannot be optimal for the insurer in realistic applications. The model is then modified by introducing a new premium rate representing the accumulated premium rates received from the existing and new customers. This model has two demand functions, i.e. power law and linear demand functions. For these demand functions, it is known that withdrawal from the market, setting a premium above the break even point, or loss leading can be optimal. Furthermore, the optimal premium strategy is sensitive to the form of the demand function. Keywords: pontryagin’s maximum principle, optimal premium strategy.