Stackelberg equilibria in monopoly insurance markets with probability weighting

Maria Andraos; Mario Ghossoub; Bin Li; Benxuan Shi

doi:10.1017/asb.2026.10106

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Stackelberg equilibria in monopoly insurance markets with probability weighting

Journal article

Open access

Peer reviewed

Stackelberg equilibria in monopoly insurance markets with probability weighting

Maria Andraos, Mario Ghossoub, Bin Li and Benxuan Shi

ASTIN Bulletin : The Journal of the IAA

06/16/2026

DOI: 10.1017/asb.2026.10106

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Abstract

We study Stackelberg equilibria (Bowley optima) in a monopolistic centralized sequential-move insurance market, with a profit-maximizing insurer who sets premia using a distortion premium principle, and a single policyholder who seeks to minimize a distortion risk measure. We show that equilibria are characterized as follows: In equilibrium, the optimal indemnity function exhibits a layer-type structure, providing full insurance over any loss layer on which the policyholder is more pessimistic than the insurer’s pricing functional about tail losses; and no insurance coverage over loss layers on which the policyholder is less pessimistic than the insurer’s pricing functional about tail losses. In equilibrium, the optimal pricing distortion function is determined by the policyholder’s degree of risk aversion, whereby prices never exceed the policyholder’s marginal willingness to insure tail losses. Moreover, we show that both the insurance coverage and the insurer’s expected profit increase with the policyholder’s degree of risk aversion. Additionally, and echoing recent work in the literature, we show that equilibrium contracts are Pareto efficient, but they do not induce a welfare gain to the policyholder. Conversely, any Pareto-optimal contract that leaves no welfare gain to the policyholder can be obtained as an equilibrium contract. Finally, we consider a few examples of interest that recover some existing results in the literature as special cases of our analysis.

Bowley optima

distortion premium principle

distortion risk measure

Pareto optima

probability weighting

Stackelberg equilibria

Details

Title: Subtitle: Stackelberg equilibria in monopoly insurance markets with probability weighting
Creators: Maria Andraos - University of Waterloo
Mario Ghossoub - University of Waterloo
Bin Li - University of Waterloo
Benxuan Shi - University of Waterloo
Resource Type: Journal article
Publication Details: ASTIN Bulletin : The Journal of the IAA
DOI: 10.1017/asb.2026.10106
ISSN: 0515-0361
eISSN: 1783-1350
Publisher: Cambridge University Press
Language: English
Electronic publication date: 06/16/2026
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9985179851102771

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