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...

In this paper we localize some of Watanabe’s results on Wiener functionals of fractional regularity, and use them to give a precise estimate of the difference between two Donsker’s delta functionals even with fractional differentiability. As an application, the convergence rate of the...

Processes with independent increments are proven to be the unique solutions of duality formulas. This result is based on a simple characterization of infinitely divisible random vectors by a functional equation in which a difference operator appears. This operator is constructed by a variational...