Abstract

Actuarial risks can be determined from aggregate claim amount processes or from aggregate surplus processes. We show how risk measures based on these processes can be efficiently evaluated through specific exponential change of measures, which are Lundberg's and the Daniel's conjugations. We first consider a compound Poisson surplus process perturbed by a Wiener Process. The measure of risk is the probability that the surplus ever crosses the null line, called probability of ruin. We show how this probability can be accurately computed by simulation under Lundberg's conjugated measure. We then consider an aggreagate claim amount Poisson process under constant force of interest and under time inhomogeneity. It is a shot-noise process, for which we propose some specific periodic intensity measures. We obtain the moment generating function of the distribution and we show how to invert it under Daniel's conjugated measure. From there, we show to obtain the tail-value-at-risk, which is a coherent measure of risk. Numerical comparisons with alternative methods illustrate the efficiency of these methods.