Non-cooperative dynamic games for general insurance markets

Boonen, Tim J, Pantelous, Athanasios A ORCID: 0000-0001-5738-1471 and Wu, Renchao (2018) Non-cooperative dynamic games for general insurance markets. INSURANCE MATHEMATICS & ECONOMICS, 78. pp. 123-135.

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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.

Item Type:	Article
Uncontrolled Keywords:	Insurance market competition, Premium cycles, Solvency ratio, Open-loop Nash equilibrium, Finite-time differential game
Depositing User:	Symplectic Admin
Date Deposited:	22 Feb 2019 11:22
Last Modified:	19 Jan 2023 01:02
DOI:	10.1016/j.insmatheco.2017.12.001
Open Access URL:	https://pure.uva.nl/ws/files/19914815/BoonenPantel...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3033261