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On a Markovian game model for competitive insurance pricing

Author

Listed:
  • Claire Mouminoux

    (BETA - Bureau d'Économie Théorique et Appliquée - AgroParisTech - UNISTRA - Université de Strasbourg - Université de Haute-Alsace (UHA) - Université de Haute-Alsace (UHA) Mulhouse - Colmar - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Christophe Dutang

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Stéphane Loisel

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Hansjoerg Albrecher

    (UNIL - Université de Lausanne = University of Lausanne)

Abstract

In this paper, we extend the non-cooperative one-period game of Dutang et al. (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.

Suggested Citation

  • Claire Mouminoux & Christophe Dutang & Stéphane Loisel & Hansjoerg Albrecher, 2021. "On a Markovian game model for competitive insurance pricing," Post-Print hal-03448339, HAL.
    • Handle: RePEc:hal:journl:hal-03448339
    DOI: 10.1007/s11009-021-09906-1
    Note: View the original document on HAL open archive server: https://hal.science/hal-03448339
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    More about this item

    Keywords

    Markov chains; Game theory; Consumers' price sensitivity; Solvency constraint; Non-cooperative game;
    All these keywords.

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