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Your search keyword '"Privault, Nicolas"' showing total 2 results
Start Over Author "Privault, Nicolas" Topic monte carlo method Publisher elsevier b.v.
2 results on '"Privault, Nicolas"'

1. Sensitivity analysis and density estimation for finite-time ruin probabilities

Author

Loisel, Stéphane and Privault, Nicolas

Subjects
*SENSITIVITY analysis, *DENSITY functionals, *ESTIMATION theory, *FINITE differences, *REVERSE mathematics, *MONTE Carlo method, *RANDOM variables, *MATHEMATICAL analysis
Abstract

Abstract: The goal of this paper is to obtain probabilistic representation formulas that are suitable for the numerical computation of the (possibly non-continuous) density functions of infima of reserve processes commonly used in insurance. In particular we show, using Monte Carlo simulations, that these representation formulas perform better than standard finite difference methods. Our approach differs from Malliavin probabilistic representation formulas which generally require more smoothness on random variables and entail the continuity of their density functions. [Copyright &y& Elsevier]

Published
2009
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2. Recursive computation of the Hawkes cumulants.

Author

Privault, Nicolas

Subjects
*MONTE Carlo method, *CUMULANTS, *DIFFERENTIAL equations, *POINT processes, *MARTINGALES (Mathematics)
Abstract

We propose a recursive method for the computation of the cumulants of self-exciting point processes of Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement on higher-order cumulants in comparison with existing methods based on differential equations, tree enumeration or martingale arguments. The results are corroborated by Monte Carlo simulations, and also apply to the computation of joint cumulants generated by multidimensional self-exciting processes. [ABSTRACT FROM AUTHOR]

Published
2021
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