Bowley-optimal convex-loaded premium principles

Mario Ghossoub, Bin Li and Benxuan Shi

Insurance: Mathematics and Economics, 2025, vol. 121, issue C, 157-180

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.

Keywords: Optimal premium principles; Expected-value premium principle; Stop-loss premium principle; Stackelberg equilibrium; Bowley optima; Dual approach (search for similar items in EconPapers)
JEL-codes: C61 C72 G22 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:121:y:2025:i:c:p:157-180

DOI: 10.1016/j.insmatheco.2025.01.006

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