Journal of Applied Probability

First passage times of (reflected) Ornstein-Uhlenbeck processes over random jump boundaries

Lijun Bo, Yongjin Wang, and Xuewei Yang

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Abstract

In this paper we study first passage times of (reflected) Ornstein-Uhlenbeck processes over compound Poisson-type boundaries. In fact, we extend the results of first rendezvous times of (reflected) Brownian motion and compound Poisson-type processes in Perry, Stadje and Zacks (2004) to the (reflected) Ornstein-Uhlenbeck case.

Article information

Source
J. Appl. Probab., Volume 48, Number 3 (2011), 723-732.

Dates
First available in Project Euclid: 23 September 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1316796910

Digital Object Identifier
doi:10.1239/jap/1316796910

Mathematical Reviews number (MathSciNet)
MR2884811

Zentralblatt MATH identifier
1239.60079

Subjects
Primary: 60J60: Diffusion processes [See also 58J65] 60K10: Applications (reliability, demand theory, etc.)

Keywords
First passage time Ornstein-Uhlenbeck process reflecting barrier compound Poisson-type boundary

Citation

Bo, Lijun; Wang, Yongjin; Yang, Xuewei. First passage times of (reflected) Ornstein-Uhlenbeck processes over random jump boundaries. J. Appl. Probab. 48 (2011), no. 3, 723--732. doi:10.1239/jap/1316796910. https://projecteuclid.org/euclid.jap/1316796910


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References

  • Alili, L., Patie, P. and Pedersen, J. L. (2005). Representations of the first hitting time density of an Ornstein-Uhlenbeck process. Stoch. Models 21, 967–980.
  • Ata, B., Harrison, J. M. and Shepp, L. A. (2005). Drift rate control of a Brownian processing system. Ann. Appl. Prob. 15, 1145–1160.
  • Bo, L., Wang, Y. and Yang, X. (2010). First passage problems on reflected generalized Ornstein-Uhlenbeck processes and applications. Preprint.
  • Bo, L., Wang, Y. and Yang, X. (2011). Some integral functionals of reflected SDEs and their applications in finance. Quant. Finance 11, 343–348.
  • Bo, L., Zhang, L. and Wang, Y. (2006). On the first passage times of reflected OU processes with two-sided barriers. Queueing Systems 54, 313–316.
  • Bo, L., Tang, D., Wang, Y. and Yang, X. (2011). On the conditional default probability in a regulated market: a structural approach. Quant. Finance, 8pp.
  • Borovkov, K. and Novikov, A. (2008). On exit times of Levy-driven Ornstein-Uhlenbeck processes. Statist. Prob. Lett. 78, 1517–1525.
  • Hadjiev, D. I. (1985). The first passage problem for generalized Ornstein-Uhlenbeck processes with non-positive jumps. In Séminaire de Probabilités XIX (Lecture Notes Math. 1123), Springer, Berlin, pp. 80–90.
  • Harrison, J. M. (1985). Brownian Motion and Stochastic Flow Systems. John Wiley, New York.
  • Itô, K. and McKean, H. P., Jr. (1996). Diffusion Processes and Their Sample Paths. Springer, Berlin.
  • Karatzas, I. and Shreve, S. E. (1991). Brownian Motion and Stochastic Calculus. Springer, New York.
  • Li, Y., Wang, Y. and Yang, X. (2010). On the hitting time density for reflected OU processes: with an application to the regulated market. Preprint.
  • Linetsky, V. (2005). On the transition densities for reflected diffusions. Adv. Appl. Prob. 37, 435–460.
  • Loeffen, R. L. and Patie, P. (2010). Absolute ruin in the Ornstein-Uhlenbeck type risk model. Preprint. available at http://arxiv.org.abs/1006.2712v1.
  • Patie, P. (2005). On a martingale associated to generalized Ornstein-Uhlenbeck processes and an application to finance. Stoch. Process. Appl. 115, 593–607.
  • Perry, D., Stadje, W. and Zacks, S. (2004). The first rendezvous time of Brownian motion and compound Poisson-type processes. J. Appl. Prob. 41, 1059–1070.
  • Protter, P. E. (2004). Stochastic Integration and Differential Equations. Springer,