Optimal Underreporting and Competitive Equilibrium

TL;DR

This paper models a dynamic insurance market with competing firms and insureds, analyzing strategic underreporting and pricing under a Bonus-Malus System, establishing existence and uniqueness of equilibrium strategies.

Contribution

It introduces a novel oligopolistic model with proven existence and uniqueness of insureds' reporting strategies and equilibrium premiums, including sensitivity analysis.

Findings

Existence and uniqueness of reporting barrier in oligopolistic setting

Nash equilibrium premium strategies for 2-class BMS

Sensitivity analysis of model parameters on equilibrium premiums

Abstract

This paper develops a dynamic insurance market model comprising two competing insurance companies and a continuum of insureds, and examines the interaction between strategic underreporting by the insureds and competitive pricing between the insurance companies under a Bonus-Malus System (BMS) framework. For the first time in an oligopolistic setting, we establish the existence and uniqueness of the insureds' optimal reporting barrier, as well as its continuous dependence on the BMS premiums. For the 2-class BMS case, we prove the existence of Nash equilibrium premium strategies and conduct an extensive sensitivity analysis on the impact of the model parameters on the equilibrium premiums.