Exit Times, Undershoots and Overshoots for Reflected CIR Process with Two-Sided Jumps

Pingping Jiang (), Bo Li () and Yongjin Wang ()
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Pingping Jiang: Nankai University
Bo Li: Nankai University
Yongjin Wang: Nankai University

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 2, 693-710

Abstract: Abstract In this paper, we investigate the reflected CIR process with two-sided jumps to capture the jump behavior and its non-negativeness. Applying the method of (complex) contour integrals, the closed-form solution to the joint Laplace transform of the first passage time crossing a lower level and the corresponding undershoot is derived. We further extend our arguments to the exit problem from a finite interval and obtain joint Laplace transforms. Our results are expressed in terms of the real and imaginary parts of complex functions by complex matrix. Numerical results are included.

Keywords: Reflected CIR jump process; Contour integrals; Exit time; Undershoot; Overshoot; 60H10; 60J75 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-019-09730-8

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