Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

Markov chains (MCs) are widely used to model a great deal of financial and actuarial problems. Likewise, they also in many other fields ranging from economics, management, agricultural sciences, engineering or informatics medicine. This paper focuses on the use MCs for design non-life bonus-malus systems (BMSs). It proposes quantifying uncertainty transition probabilities BMSs by using fuzzy numbers (FNs). To do so, Fuzzy (FMCs) as defined Buckley Eslami 2002 used, thus giving rise concept (FBMSs). More concretely, we describe detail common BMS where number claims follows Poisson distribution under hypothesis that its characteristic parameter is not real but triangular FN (TFN). Moreover, reflect how fit several data analysis tools discuss goodness approximates probabilities, stationary state, mean asymptotic premium. The FMCs allows obtaining only point estimates all these variables, structured set their possible values whose reliability given means possibility measure. Although our circumscribed insurance, findings can easily be extended any abovementioned with slight modifications.