Pricing in a competitive stochastic insurance market

Abstract This paper studies a one-period stochastic game to determine the optimal premium strategies of non-life insurers in competitive market. Specifically, strategy is determined by Nash equilibrium an n -player game, which each player assumed maximise expected utility terminal wealth. The wealth stochastic, since number policies and size claims are considered be random variables. total loss insurer described collective risk model. affected all premiums market further investigated two distinct demand functions. Both models have exponential functional form, that characterised price sensitivity parameters. first model zero for above given threshold, whereas second does not include such restriction. pure as solutions constrained optimisation problems. For we prove existence uniqueness equilibrium, provide formula when it exists. Two numerical examples provided illustrate applicability our findings.