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