The GAEP algorithm for the fast computation of the distribution of a function of dependent random variables

Abstract

We introduce a new algorithm for numerically computing the distribution of an increasing function of d dependent, non-negative random variables with a given joint distribution. We prove the convergence of the algorithm and give convergence rates under regularity conditions.

Keywords:

• convolution
• distribution functions
• dependent random variables

AMS Subject Classification::

• 62E17
• 65C20
• 65C50

Acknowledgements

The authors thank Guus Balkema for some useful comments on a previous version of this paper. Philipp Arbenz, as SCOR Fellow, thanks SCOR Switzerland for the financial support. Paul Embrechts, as Senior SFI Professor, acknowledges the support from the Swiss Finance Institute. Giovanni Puccetti would like to thank RiskLab and the Forschungsinstitut für Mathematik (FIM) of the Department of Mathematics, ETH Zurich, for the financial support.