Sensitivity analysis and density estimation for finite-time ruin probabilities

Stéphane Loisel (1) , Nicolas Privault (2)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 CUHK - City University of Hong Kong [Hong Kong]

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 standard Malliavin probabilistic representation techniques which generally require more smoothness on random variables, entailing the continuity of their density functions.

Mots clés: Ruin probability; Malliavin calculus; insurance; integration by parts

Domaines: Economies et finances

Stéphane Loisel, Nicolas Privault. Sensitivity analysis and density estimation for finite-time ruin probabilities. 2007. ⟨hal-00201347v1⟩