Competitive insurance pricing strategies for multiple lines of business: a game-theoretic approach

Abstract

This paper explores an insurance market with insurers competing in multiple lines of business over a finite time horizon. They set premiums for single lines of business, whereas in a multi-policy contract, a discount is applied to the total sum of the single premiums. To illustrate the combinatorial components of the weighted average market premium, Young tableaux are used. We use the collective risk model to define insurers' aggregate loss, with claim amounts independent of distinct lines of business but dependent on the state of the environment. Our dynamic insurance game falls into the category of multi-stage games with observed actions. In this framework, we characterize the open-loop and closed-loop equilibrium premium profiles.