title: Game theoretical approaches for pricing of Non-life insurance policies into a competitive market environment
Creators: name: Wu, R
Publisher: name: University of Liverpool Repository
Year: 2017

description: Standard actuarial approaches for non-life insurance products suggest that the premium is divided into three main components: the actuarial price, the safety loading, and the loading for expenses. The number of product-specific policies from different companies has increased significantly, and strong market competition has boosted the demand for a competitive premium in global insurance market. Thus, the actuarial premium could eventually be altered by an insurer's marketing and management department regarding the competitive environment. Thus in this thesis, considering the competition in insurance market, game theoretical approaches are applied to investigate the influence of competition on general insurance pricing. Firstly, a two-period deterministic N-player game is formulated to investigate the optimal pricing strategy by calculating the Nash equilibrium in an insurance market. Under that framework, each insurer is assumed to maximise its utility of wealth over the unit time interval. By analyzing the competition between each pair of insurers, the whole markets' competition is characterized through an aggregation. With the purpose of solving a game of N-players, the best-response potential game with non-linear aggregation is implemented. The existence of a Nash equilibrium is proved by finding a potential function of all insurers' payoff functions. A 12-player insurance game illustrates the theoretical findings under the framework in which the best-response selection premium strategies always provide the global maximum value of the corresponding payoff function. Secondly, deterministic differential games are constructed with the purpose of studying the insurers' equilibrium premium in a competitive market. We apply an optimal control theory to determine the open-loop Nash equilibrium premium strategies. In this direction, two models are formulated and studied. The market power of each insurance company is characterized by a price sensitive parameter, and the business volume is affected by the solvency ratio. Considering the average market premiums, the first model studies an exponential relation between premium strategies and volume of business. The other model initially characterizes the competition between any selected pair of insurers, then aggregates all the paired competitions in the market. Numerical examples illustrate the premium dynamics, and show that premium cycles may exist in equilibrium. Thirdly, a multi-stage stochastic game will be constructed. Insurers are considered to be risk-averse, that is, insurers will to set risk-premiums on their products with the purpose of avoiding risk. Mean-variance Utility function will be adopted. The expenditures of insurance companies will be discussed separately as exposure related costs and non-exposure related costs. The expenditures of insurance companies will be discussed separately as exposure related costs and non-exposure-based costs. The exposure-based component is assumed to be stochastic. Finally, summary of the conclusions complete the thesis.