Boundary Crossing Probabilities of Jump Diffusion Processes to Time-Dependent Boundaries

Tung-Lung Wu ()
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Tung-Lung Wu: Mississippi State University

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 1, 13-24

Abstract: Abstract The finite Markov chain imbedding technique has been used to compute the boundary crossing probabilities of one and higher-dimensional Brownian motion. The idea is to cast the boundary crossing probabilities as the limiting probabilities of a finite Markov chain entering a set of absorbing states induced by the boundaries. In this manuscript, we extend the technique to compute the boundary crossing probabilities of a class of jump diffusion processes to time-dependent boundaries. We allow the jump sizes to have general distributions and the boundaries to be non-linear. Numerical examples are given to illustrate our theoretical results.

Keywords: Finite Markov chain imbedding; Boundary crossing probability; First passage time; Jump diffusion processes; Compound poisson processes; Brownian motion; Primary 60J65; Secondary 60J70; 60J60; 60J10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-018-9685-5

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