Ecuaciones de recurrencia estocásticas en el cálculo de la prima de reaseguro Finite Risk.

Abstract

The aim of this paper is to calculate the renewal premium of finite risk reinsurance under the assumption that the interest rate shows a stochastic evolution. The problem of the convolution of the random variables involved in the calculation of the premium has been solved by simulating claim paths using the Monte-Carlo method and applying three financial decision criteria: the expected value, the variance and the standard deviation. In the last two criteria we propose to use a stochastic recurrence equation to avoid the problem of dependence between stochastic capitalization factors. The application of the variance criterion and of the standard deviation criterion has allowed us to obtain the reinsurance premium depending on the level of risk aversion of the reinsurer and the volatility of the interest rate.