Optimal premium pricing strategies for competitive general insurance markets

Non-life insurance pricing depends on different costs including claim and business acquisition costs, management expenses and other parameters such as margins for fluctuations in claims experience, expected profits etc. Nevertheless, in a competitive insurance market environment, the company’s premium should respond to changes in the level of premiums being offered by competitors. In this paper, two major topics are being investigated. More specifically, it is crucial to explore the ways a company’s optimal strategy can be determined in a competitive market and then establish a connection between this strategy and market’s competition. Under this perspective, a general functional equation for the volume of business is proposed, which is related to the past year’s experience, the average premium of the market, the company’s premium, its reputation, and a stochastic disturbance, as a non-straightforward extension to the ideas proposed by Pantelous and Passalidou (2013). Then, using a linear discounted function for measuring the company’s wealth, an optimal premium strategy can be found which maximizes the present value of a wealth function in a discrete-time, stochastic framework. One significant characteristic of our approach is its suitability for both negative and positive effects to the volume of business depending on the company’s reputation. Furthermore, analytical solutions for some special and common cases are presented here, where the optimal premium endogenously depends on the dynamics of the market. Finally, an application based on data from the Greek insurance market which illustrates the main theoretical findings is presented for a better understanding of the model.