On a Markovian Game Model for Competitive Insurance Pricing

Claire Mouminoux, Christophe Dutang (), Stéphane Loisel and Hansjoerg Albrecher
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Claire Mouminoux: Université de Strasbourg, Université de Lorraine, CNRS, BETA
Christophe Dutang: Université Paris-Dauphine, Université PSL, CNRS, CEREMADE
Stéphane Loisel: Univ Lyon - Université Claude Bernard Lyon 1, ISFA, Laboratoire SAF EA2429
Hansjoerg Albrecher: Université de Lausanne and Swiss Finance Institute

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 2, 1061-1091

Abstract: Abstract In this paper, we extend the non-cooperative one-period game of Dutang et al. (Journal of Operational Research 231(3):702–711, 2013) to model a non-life insurance market over several periods by considering the repeated (one-period) game. Using Markov chain methodology, we derive general properties of insurer portfolio sizes given a price vector. In the case of a regulated market (identical premium), we are able to obtain convergence measures of long run market shares. We also investigate the consequences of the deviation of one player from this regulated market. Finally, we provide some insights of long-term patterns of the repeated game as well as numerical illustrations of leadership and ruin probabilities.

Keywords: Game theory; Non-cooperative game; Consumers’ price sensitivity; Solvency constraint; Markov chains; MSC 60J10; MSC 91G05; MSC 91A20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09906-1

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