@misc{10481/68060,
year = {2021},
url = {http://hdl.handle.net/10481/68060},
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.},
organization = {University of Barcelona},
publisher = {MDPI},
keywords = {Bonus-malus system},
keywords = {Fuzzy number},
keywords = {Fuzzy transition probability},
keywords = {Fuzzy Markov chain},
keywords = {Fuzzy stationary state},
title = {Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance},
doi = {10.3390/math9040347},
author = {Villacorta Iglesias, Pablo José and González-Vila Puchades, Laura and de Andrés-Sánchez, Jorge},
}