Autor según el artículo: Villacorta, Pablo J.; Gonzalez-Vila Puchades, Laura; de Andres-Sanchez, Jorge;

Departamento: Gestió d'Empreses

Autor/es de la URV: De Andrés Sànchez, Jorge

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

Resumen: 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.

Áreas temáticas: Química Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics Engineering (miscellaneous) Computer science (miscellaneous) Astronomia / física

Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/

Direcció de correo del autor: jorge.deandres@urv.cat

Identificador del autor: 0000-0002-7715-779X

Fecha de alta del registro: 2023-02-19

Versión del articulo depositado: info:eu-repo/semantics/publishedVersion

Enlace a la fuente original: https://www.mdpi.com/2227-7390/9/4/347

URL Documento de licencia: http://repositori.urv.cat/ca/proteccio-de-dades/

Referencia al articulo segun fuente origial: Mathematics. 9 (4): 1-23

Referencia 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 del artículo: 10.3390/math9040347

Entidad: Universitat Rovira i Virgili

Año de publicación de la revista: 2021

Tipo de publicación: Journal Publications