A Malliavin calculus approach to sensitivity analysis in insurance

Using the Malliavin calculus on Poisson space and a method initiated by Fournié et al. [Fournié, 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.