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The Existence of the Density of the Ruin Time for the Sum of Two Compound Poisson Processes Perturbed by a Diffusion
Last modified: 2014-02-27
Abstract
Let $(X_t, t\geq 0)$ be sum of a Brownian motion and a two
independent compound Poisson processes and $\bar{\tau}_x$ the
first hitting time of fixed level $x>0$ by this stochastic process.
We show existence of density with respect to Lebesgue measure. Link with ruin theory is also
presented.
independent compound Poisson processes and $\bar{\tau}_x$ the
first hitting time of fixed level $x>0$ by this stochastic process.
We show existence of density with respect to Lebesgue measure. Link with ruin theory is also
presented.
Keywords
Brownian motion; jump diffusion process; first passage time law