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Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

Author

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  • Pablo J. Villacorta

    (Department of Computer Science and Artificial Intelligence, Higher Technical School of Computer and Telecommunication Engineering, University of Granada, Cuesta del Hospicio s/n, 18071 Granada, Spain)

  • Laura González-Vila Puchades

    (Department of Mathematics for Economics, Finance and Actuarial Science, Faculty of Economics and Business, University of Barcelona, Avinguda Diagonal 690, 08034 Barcelona, Spain)

  • Jorge de Andrés-Sánchez

    (Social and Business Research Laboratory, Campus Bellisens, Rovira i Virgili University, Avinguda de la Universitat 1, 43204 Reus, Spain)

Abstract

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.

Suggested Citation

  • Pablo J. Villacorta & Laura González-Vila Puchades & Jorge de Andrés-Sánchez, 2021. "Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance," Mathematics, MDPI, vol. 9(4), pages 1-23, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:347-:d:496604
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    References listed on IDEAS

    as
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