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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Mississippi State University, Starkville, MS, 39759, USA

    Tung-Lung Wu

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  1. Tung-Lung Wu
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Correspondence to Tung-Lung Wu.

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Wu, TL. Boundary Crossing Probabilities of Jump Diffusion Processes to Time-Dependent Boundaries. Methodol Comput Appl Probab 22, 13–24 (2020). https://doi.org/10.1007/s11009-018-9685-5

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  • DOI: https://doi.org/10.1007/s11009-018-9685-5

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