University of Granada Researchers Add New Findings in the Area of Mathematics (Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance)

2021 FEB 18 (NewsRx) -- By a News Reporter-Staff News Editor at Insurance Daily News -- Investigators publish new report on mathematics. According to news reporting out of Granada, Spain, by NewsRx editors, research stated, “Markov chains (MCs) are widely used to model a great deal of financial and actuarial problems.”

Our news journalists obtained a quote from the research from University of Granada: “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.”

According to the news reporters, the research concluded: “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.”

For more information on this research see: Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance. Mathematics, 2021,9(347):347. (Mathematics - http://www.mdpi.com/journal/mathematics). The publisher for Mathematics is MDPI AG.

A free version of this journal article is available at https://doi.org/10.3390/math9040347.

Our news editors report that additional information may be obtained by contacting Pablo J. Villacorta Iglesias, 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. Additional authors for this research include Laura Gonzalez-Vila Gonzalez-Vila Puchades, Jorge de Andres-Sanchez.

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