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Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

  • Dades identificatives

    Identificador: imarina:9178055
    Autors:
    Villacorta, Pablo J.Gonzalez-Vila Puchades, Laurade Andres-Sanchez, Jorge
    Resum:
    Markov chains (MCs) are widely used to model a great deal of financial and actuarial problems. Likewise, they are also used in many other fields ranging from economics, management, agricultural sciences, engineering or informatics to medicine. This paper focuses on the use of MCs for the design of non-life bonus-malus systems (BMSs). It proposes quantifying the uncertainty of transition probabilities in BMSs by using fuzzy numbers (FNs). To do so, Fuzzy MCs (FMCs) as defined by Buckley and Eslami in 2002 are used, thus giving rise to the concept of Fuzzy BMSs (FBMSs). More concretely, we describe in detail the common BMS where the number of claims follows a Poisson distribution under the hypothesis that its characteristic parameter is not a real but a triangular FN (TFN). Moreover, we reflect on how to fit that parameter by using several fuzzy data analysis tools and discuss the goodness of triangular approximates to fuzzy transition probabilities, the fuzzy stationary state, and the fuzzy mean asymptotic premium. The use of FMCs in a BMS allows obtaining not only point estimates of all these variables, but also a structured set of their possible values whose reliability is given by means of a possibility measure. Although our analysis is circumscribed to non-life insurance, all of its findings can easily be extended to any of the abovementioned fields with slight modifications.
  • Altres:

    Autor segons l'article: Villacorta, Pablo J.; Gonzalez-Vila Puchades, Laura; de Andres-Sanchez, Jorge;
    Departament: Gestió d'Empreses
    Autor/s de la URV: De Andrés Sànchez, Jorge
    Paraules clau: Fuzzy transition probability Fuzzy stationary state Fuzzy number Fuzzy markov chain Bonus-malus system
    Resum: Markov chains (MCs) are widely used to model a great deal of financial and actuarial problems. Likewise, they are also used in many other fields ranging from economics, management, agricultural sciences, engineering or informatics to medicine. This paper focuses on the use of MCs for the design of non-life bonus-malus systems (BMSs). It proposes quantifying the uncertainty of transition probabilities in BMSs by using fuzzy numbers (FNs). To do so, Fuzzy MCs (FMCs) as defined by Buckley and Eslami in 2002 are used, thus giving rise to the concept of Fuzzy BMSs (FBMSs). More concretely, we describe in detail the common BMS where the number of claims follows a Poisson distribution under the hypothesis that its characteristic parameter is not a real but a triangular FN (TFN). Moreover, we reflect on how to fit that parameter by using several fuzzy data analysis tools and discuss the goodness of triangular approximates to fuzzy transition probabilities, the fuzzy stationary state, and the fuzzy mean asymptotic premium. The use of FMCs in a BMS allows obtaining not only point estimates of all these variables, but also a structured set of their possible values whose reliability is given by means of a possibility measure. Although our analysis is circumscribed to non-life insurance, all of its findings can easily be extended to any of the abovementioned fields with slight modifications.
    Àrees temàtiques: Química Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics Engineering (miscellaneous) Computer science (miscellaneous) Astronomia / física
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: jorge.deandres@urv.cat jorge.deandres@urv.cat
    Identificador de l'autor: 0000-0002-7715-779X 0000-0002-7715-779X
    Data d'alta del registre: 2024-07-27
    Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
    Enllaç font original: https://www.mdpi.com/2227-7390/9/4/347
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referència a l'article segons font original: Mathematics. 9 (4): 1-23
    Referència de l'ítem segons les normes APA: Villacorta, Pablo J.; Gonzalez-Vila Puchades, Laura; de Andres-Sanchez, Jorge; (2021). Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance. Mathematics, 9(4), 1-23. DOI: 10.3390/math9040347
    DOI de l'article: 10.3390/math9040347
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2021
    Tipus de publicació: Journal Publications
  • Paraules clau:

    Computer Science (Miscellaneous),Engineering (Miscellaneous),Mathematics,Mathematics (Miscellaneous)
    Fuzzy transition probability
    Fuzzy stationary state
    Fuzzy number
    Fuzzy markov chain
    Bonus-malus system
    Química
    Mathematics (miscellaneous)
    Mathematics (all)
    Mathematics
    General mathematics
    Engineering (miscellaneous)
    Computer science (miscellaneous)
    Astronomia / física
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