Joint Hitting-Time Densities for Finite State Markov Processes

Abstract

For a finite state Markov process and a finite collection $\{{\Gamma }_k,k\in K\}$ of subsets of its state space, let ${\tau }_k$ be the first time the process visits the set ${\Gamma }_k$. We derive explicit/recursive formulas for the joint density and tail probabilities of the stopping times $\{{\tau }_k,k\in K\}$. The formulas are natural generalizations of those associated with the jump times of a simple Poisson process. We give a numerical example and indicate the relevance of our results to credit risk modeling.

25 pages, 3 figures

References in corpus (1)

• Credit contagion and risk management with multiple non-ordered defaults