On a Markovian game model for competitive insurance pricing

Claire Mouminoux (1) , Christophe Dutang (2) , Stéphane Loisel (3) , Hansjoerg Albrecher (4)

1 BETA - Bureau d'Économie Théorique et Appliquée
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 SAF - Laboratoire de Sciences Actuarielle et Financière
4 UNIL - Université de Lausanne = University of Lausanne

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.

Mots clés: Markov chains; Game theory; Consumers' price sensitivity; Solvency constraint; Non-cooperative game

Domaines: Statistiques [math.ST]; Calcul [stat.CO]; Applications [stat.AP]; Finance quantitative [q-fin.CP]

Claire Mouminoux, Christophe Dutang, Stéphane Loisel, Hansjoerg Albrecher. On a Markovian game model for competitive insurance pricing. Methodology and Computing in Applied Probability, 2021, ⟨10.1007/s11009-021-09906-1⟩. ⟨hal-03448339⟩