A Malliavin calculus approach to sensitivity analysis in insurance

Using the Malliavin calculus on Poisson space and a method initiated by Fournie et al. [Fournie, E., Lasry, J.M., Lebuchoux, J., Lions, P.L., Touzi, N., 1999. Applications of Malliavin calculus to Monte Carlo methods in finance. Finance Stochastics 3, 391-412.] for continuous financial markets, we compute the probability density of risk reserve processes and the sensitivities of probabilities of ruin at a given date for insurance portfolios under interest force. The simulation graphs provided show that this method is computationally more efficient than the standard approximation of derivatives by finite differences. (C) 2004 Elsevier B.V. All rights reserved.