On a Markovian game model for competitive insurance pricing

Autor: Christophe Dutang, Claire Mouminoux, Hansjoerg Albrecher, Stéphane Loisel
Přispěvatelé: Bureau d'Économie Théorique et Appliquée (BETA), Université de Strasbourg (UNISTRA)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de Sciences Actuarielle et Financière (SAF), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Université de Lausanne (UNIL)
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Statistics and Probability
Markov chains Mathematics Subject Classification (2010): MSC 91A20
General Mathematics
Markov process
Markov chains Mathematics Subject Classification (2010): MSC 60J10
01 natural sciences
Solvency constraint
[QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP]
010104 statistics & probability
symbols.namesake
Consumers' price sensitivity
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
0502 economics and business
0101 mathematics
Market share
[STAT.CO]Statistics [stat]/Computation [stat.CO]
Game theory
Markov chains Mathematics Subject Classification (2010): MSC 91G05
Mathematics
Non-cooperative game
[STAT.AP]Statistics [stat]/Applications [stat.AP]
050208 finance
Markov chain
Early Access OCT 2021
05 social sciences
Regulated market
Repeated game
symbols
Portfolio
Mathematical economics
Zdroj: Methodology and Computing in Applied Probability
Methodology and Computing in Applied Probability, Springer Verlag, 2021, ⟨10.1007/s11009-021-09906-1⟩
ISSN: 1387-5841
1573-7713
DOI: 10.1007/s11009-021-09906-1⟩
Popis: 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.
Databáze: OpenAIRE
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