Bowley-optimal convex-loaded premium principles

Abstract

This paper contributes to the literature on Stackelberg equilibria (Bowley optima) in monopolistic centralized sequential-move insurance markets in several ways. We consider a class of premium principles defined as expectations of increasing and convex functions of the indemnities. We refer to these as convex-loaded premium principles. Our analysis restricts the ex ante admissible class of indemnity functions to the two most popular and practically relevant classes: the deductible indemnities and the proportional indemnities, both of which satisfy the so-called no-sabotage condition. We study Bowley optimality of premium principles within the class of convex-loaded premium principles, when the indemnity functions are either of the deductible type or of the coinsurance type. Assuming that the policyholder is a risk-averse expected-utility maximizer, while the insurer is a risk-neutral expected-profit maximizer, we find that the expected-value premium principle is Bowley optimal for proportional indemnities, while the stop-loss premium principle is Bowley optimal for deductible indemnities under a mild condition. Methodologically, we introduce a novel dual approach to characterize Bowley optima.