Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

Pablo J. Villacorta, Laura González-Vila Puchades and Jorge de Andrés-Sánchez
Additional contact information
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

Mathematics, 2021, vol. 9, issue 4, 1-23

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.

Keywords: bonus-malus system; fuzzy number; fuzzy transition probability; fuzzy Markov chain; fuzzy stationary state (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/4/347/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/4/347/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:4:p:347-:d:496604

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().