Joint Hitting-Time Densities for Finite State Markov Processes

2014/02/27 by Tomasz R. Bielecki, Bielecki, Tomasz R., Monique Jeanblanc +3
Decision Sciences · Economics, Econometrics and Finance · #60G40 #60J27 #91G40 #Credit Risk and Financial Regulations #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1402.7093

openalex publication_date 2014/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a finite state Markov process and a finite collection \ Γ_k, k ∈ K \ of subsets of its state space, let τ_k be the first time the process visits the set Γ_k. We derive explicit/recursive formulas for the joint density and tail probabilities of the stopping times \ τ_k, k ∈ 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.

Citations

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

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