A Malliavin Calculus Approach to Sensitivity Analysis in Insurance

15 Pages Posted: 16 May 2004  

Nicolas Privault

Université de la Rochelle

Xiao Wei

Wuhan University - Department of Mathematics

Date Written: July 23, 2003

Abstract

Using the Malliavin calculus on Poisson space we compute the probability density of risk reserve processes and the sensitivities of probabilities of ruin at a given date for an insurance portfolio under interest force. We follow a method initiated in Fournie et al. Finance and Stochastics 3(4) 391-412, 1999, for continuous financial markets. The simulation graphs provided show that this method is computationally more efficient than the classical finite-difference Monte-Carlo approximation of derivatives.

Keywords: Probabilities of ruin, reserve processes, sensitivity analysis, Malliavin calculus

JEL Classification: G22

Suggested Citation

Privault, Nicolas and Wei, Xiao, A Malliavin Calculus Approach to Sensitivity Analysis in Insurance (July 23, 2003). Available at SSRN: https://ssrn.com/abstract=546862 or http://dx.doi.org/10.2139/ssrn.546862

Nicolas Privault (Contact Author)

Université de la Rochelle ( email )

Avenue Marillac
Department of Mathematics
F-17042 La Rochelle Cedex 1
France

HOME PAGE: http://perso.univ-lr.fr/nprivaul/

Wei Xiao

Wuhan University - Department of Mathematics ( email )

Wuhan
China

Paper statistics

Downloads
161
Rank
151,759
Abstract Views
785