Probabilidade da ruÃna no mercado de seguros: fundamentos teÃricos e alguns resultados de simulaÃÃo

AUTOR(ES)

Silvia Regina Ribeiro Lemos

DATA DE PUBLICAÇÃO

2008

RESUMO

In this work the theoretical basis for modeling the ruin of an insurance company is presented. We studied the classic CramÃr-Lundberg risk model, which uses an homogeneous Poisson process to model the number of claims that arrives to an insurance company during a given period t of time. Also, different types of probability distributions, that can be used to model an eventual insurance company ruin, and some approximations to the probability of ruin, such as De Vylder,Beekman-Bowers and CramÃr-Lundberg, are presented. In addition, we describe the Erik Sparre Andersen classic risk model, which is an extension of the CramÃr-Lundberg model, and we use it to calculate the probability of a ruin in continuous time and infinite temporal horizon. The results of the simulation lead to conclusions which are similar to those found in the literature, in the sense that one can not state that there is the best approximation to the probability of a ruin, as it depends not only on the used probability distributions but also on their parameter values. The simulation results also shown that, when the time between different claims has a gamma density function, the simulated estimates of the probability of ruin converge more quickly to zero when the refunds have a light-tail density function then when refunds have a heavy-tail density function

ASSUNTO(S)

probabilidade da ruÃna cramÃr-lundberg cramÃr-lundberg risco de seguradora insurance risk ruin probability estatistica

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