Lexuri FERNANDEZ, ISBA, UCL

Dependence Structures of Marshall--Olkin Kind.

Abstract:

The probability distribution of the mean of default times, which are dependent under the Marshall--Olkin law, is computed. The Marshall--Olkin distribution is a core probability law in reliability and life-testing applications. Exact expressions for the distribution of the mean of default times are derived in the general bivariate case and for low dimensions in the exchangeable one. When the dimension tends to infinity, we prove that the mean of these dependent default times converges to the exponential functional of a Lévy subordinator. Finally, different simulation techniques to simulate Lévy-frailty copulas, which are built from an alpha-stable Lévy subordinator, are analyzed in terms of computational speed. The possibility to simulate these copulas in an efficient way allows us to numerically compute, with a low computational cost, the exponential functional of a Lévy subordinator.

Lexuri Fernández - joint work with Matthias Scherer -