دانلود رایگان مقاله بازی های غیرتعاونی و پویا برای بازارهای بیمه کل

abstract

In the insurance industry, the number of product-specific policies from different companies has increased significantly. The strong market competition has boosted the demand for a competitive premium. In actuarial science, scant literature still exists on how competition actually affects the calculation and the cycles of company’s premiums. In this paper, we model premium dynamics via differential games, and study the insurers’ equilibrium premium dynamics in a competitive market. We apply an optimal control theory methodology to determine the open-loop Nash equilibrium premium strategies. The market power of each insurance company is characterized by a price sensitive parameter, and the business volume is affected by the solvency ratio. We study two models. Considering the average market premiums, the first model studies an exponential relation between premium strategies and volume of business. The second model initially characterizes the competition between any selected pair of insurers, and then aggregates all the paired competitions in the market. Numerical examples illustrate the premium dynamics, and show that premium cycles may exist in equilibrium.

5. Conclusion

This paper studies two finite-time differential games in an insurance market. It provides how competition impacts the premium process of non-life insurance products. An optimal control theory approach is applied to determine premiums in the open-loop Nash Equilibrium. The first model (Model I) adopts the exponential demand function proposed by Taylor (1986, 1987) and Emms(2012), and the second model (Model II) is formulated based on the aggregate exposure proposed by Wu and Pantelous (2017). Numerical examples illustrate the premium dynamics, and show that premium cycles do exist in equilibrium for the Model II. As a future research, we are interested in applying stochastic models to dynamic games. Another possible extension would be to study feedback Nash equilibria for dynamic games.