Sensitivity analysis and density estimation for finite-time ruin probabilities

The goal of this paper is to obtain probabilistic representation formulas that are suitable for the numerical computation of the (possibly non-continuous) density functions of infima of reserve processes commonly used in insurance. In particular we show, using Monte Carlo simulations, that these representation formulas perform better than standard finite difference methods. Our approach differs from Malliavin probabilistic representation formulas which generally require more smoothness on random variables and entail the continuity of their density functions.