Optimal Premium Pricing in a Competitive Stochastic Insurance Market with Incomplete Information: A Bayesian Game-theoretic Approach
Insurance: Mathematics and Economics, Volume 119, pp. 32-47. November 2024, DOI: 10.1016/j.insmatheco.2024.07.006
51 Pages Posted: 18 Aug 2023
Date Written: August 14, 2023
Abstract
This paper examines a stochastic one-period insurance market with incomplete information. The aggregate amount of claims follows a compound Poisson distribution. Insurers are assumed to be exponential utility maximizers, with their degree of risk aversion forming their private information. A premium strategy is defined as a mapping between risk-aversion types and premium rates. The optimal premium strategies are denoted by the pure-strategy Bayesian Nash equilibrium, whose existence and uniqueness are demonstrated under specific conditions on the insurer-specific demand functions. Boundary and monotonicity properties for equilibrium premium strategies are derived.
Keywords: Competitive Insurance Markets, Incomplete Information, Bayesian Nash Equilibrium, Combined Ratio. JEL classification: G22, C72, C73, C11
JEL Classification: G22, C72, C73, C11
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