Author, as appears in the article.: Villacorta, Pablo J.; Gonzalez-Vila Puchades, Laura; de Andres-Sanchez, Jorge;

Department: Gestió d'Empreses

URV's Author/s: De Andrés Sànchez, Jorge

Keywords: Fuzzy transition probability Fuzzy stationary state Fuzzy number Fuzzy markov chain Bonus-malus system

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.

Thematic Areas: Química Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics Engineering (miscellaneous) Computer science (miscellaneous) Astronomia / física

licence for use: https://creativecommons.org/licenses/by/3.0/es/

Author's mail: jorge.deandres@urv.cat

Author identifier: 0000-0002-7715-779X

Record's date: 2023-02-19

Papper version: info:eu-repo/semantics/publishedVersion

Link to the original source: https://www.mdpi.com/2227-7390/9/4/347

Licence document URL: http://repositori.urv.cat/ca/proteccio-de-dades/

Papper original source: Mathematics. 9 (4): 1-23

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

Article's DOI: 10.3390/math9040347

Entity: Universitat Rovira i Virgili

Journal publication year: 2021

Publication Type: Journal Publications