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Some Explicit Results on First Exit Times for a Jump Diffusion Process Involving Semimartingale Local Time

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  • Shiyu Song

    (Tianjin University)

Abstract

In this paper, we consider the one-sided and the two-sided first exit problem for a jump diffusion process with semimartingale local time. Denote this process by $$X=\{X_{t},t\ge 0\}$$ X = { X t , t ≥ 0 } and set $$\tau _{l}=\inf \{t\ge 0, X_{t}\le l\}$$ τ l = inf { t ≥ 0 , X t ≤ l } and $$\tau _{l,u}=\inf \{t\ge 0, X_{t}\notin (l,u)\}$$ τ l , u = inf { t ≥ 0 , X t ∉ ( l , u ) } with $$l

Suggested Citation

  • Shiyu Song, 2021. "Some Explicit Results on First Exit Times for a Jump Diffusion Process Involving Semimartingale Local Time," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2346-2367, December.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:4:d:10.1007_s10959-020-01040-x
    DOI: 10.1007/s10959-020-01040-x
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    References listed on IDEAS

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    1. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    2. Borovkov, Konstantin & Novikov, Alexander, 2008. "On exit times of Lévy-driven Ornstein-Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1517-1525, September.
    3. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    4. Jacobsen, Martin & Jensen, Anders Tolver, 2007. "Exit times for a class of piecewise exponential Markov processes with two-sided jumps," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1330-1356, September.
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