References
- Göing-Jaeschke, A. , Yor, M. (2003). A clarification note about hitting times densities for Ornstein-Uhlenbeck processes. Finance and Stochastics . 7(3) :413–415.
- Ricciardi, L. M. , Sato, S. (1988). First-passage-time density and moments of the Ornstein-Uhlenbeck process. J. Appl. Probab. 25(1) :43–57.
- Yi, C. (2010). On the first passage time distribution of an Ornstein-Uhlenbeck process. Quantitative Finance . 10(9):957–960.
- Leblanc, B. , Renault, O. , Scaillet, O. (2000). A correction note on the first passage time of an Ornstein-Uhlenbeck process to a boundary. Finance and Stochastics . 4(1) :109–111.
- Pitman, J., Yor, M. (1981). Bessel processes and infinitely divisible laws. In: Williams, D., ed. Stochastic Integrals. Lecture Notes in Mathematics, Vol. 851., Berlin, Heidelberg: Springer.
- Pitman, J. , Yor, M. (1982). A decomposition of Bessel bridges. Z. Wahrscheinlichkeitstheorie Verw Gebiete . 59(4):425–457.
- Alili, L. , Patie, P. , Pedersen, J. L. (2005). Representations of the first hitting time density of an Ornstein-Uhlenbeck process. Stoch Models . 21(4):967–980.
- Patie, P. (2004). On some first passage time problems motivated by financial applications (Doctoral dissertation, Universität Zürich).
- Linetsky, V. (2004b). Computing hitting time densities for CIR and OU diffusions: applications to mean-reverting models. JCF . 7(4):1–22.
- Linetsky, V. (2004a). Lookback options and diffusion hitting times: A spectral expansion approach. Finance and Stochastics . 8(3):373–398.
- Tuckwell, H. C. , Wan, F. Y. (1984). First-passage time of Markov processes to moving barriers. J. Appl. Probab. 21(4):695–709.
- Durbin, J. (1985). The first-passage density of a continuous Gaussian process to a general boundary. J. Appl. Probab . 22(01):99–122.
- Durbin, J. , Williams, D. (1992). The first-passage density of the Brownian motion process to a curved boundary. J. Appl. Probab . 29(02):291–304.
- Buonocore, A. , Nobile, A. G. , Ricciardi, L. M. (1987). A new integral equation for the evaluation of first-passage-time probability densities. Adv. Appl. Probab. 19(4):784–800.
- Di Nardo, E. , Nobile, A. G. , Pirozzi, E. , Ricciardi, L. M. (2001). A computational approach to first-passage-time problems for Gauss-Markov processes. Adv. Appl. Probab. 33(2):453–482.
- Giorno, V. , Nobile, A. G. , Ricciardi, L. M. , Sato, S. (1989). On the evaluation of first-passage-time probability densities via non-singular integral equations. Adv. Appl. Probab. 21(1):20–36.
- Lehmann, A. (2002). Smoothness of first passage time distributions and a new integral equation for the first passage time density of continuous Markov processes. Adv. Appl. Probab. 34(4):869–887.
- Gutiérrez, R. , Ricciardi, L. M. , Román, P. , Torres, F. (1997). First-passage-time densities for time-non-homogeneous diffusion processes. J. Appl. Probab. 34(3) :623–631.
- Karlin, S. , Taylor, H. E. (1981). A Second Course in Stochastic Processes . New York: Academic Press.
- Wenocur, M. L. (1987). Diffusion first passage times: approximations and related differential equations. Stochastic Processes Appl. 27 :159–177.
- Lo, C. F. , Hui, C. H. (2006). Computing the first passage time density of a time-dependent Ornstein-Uhlenbeck process to a moving boundary. Appl. Math. Lett. 19(12) :1399–1405.
- Hernandez-del-Valle, G. (2012). On the first time that an Ito process hits a barrier. arXiv preprint arXiv:1209.2411.
- Lipton, A. , Kaushansky, V. (2018). On the first hitting time density of an Ornstein-Uhlenbeck Process. arXiv:1810.02390v2.
- Martin, R. J. , Kearney, M. J. , Craster, R. V. (2019). Long- and short-time asymptotics of the first-passage time of the Ornstein-Uhlenbeck and other mean-reverting processes. J. Phys. A: Math. Theor . 52(13):134001.
- Kent, J. T. (1980). Eigenvalue expansion for diffusion hitting times. Z. Wahrscheinlichkeitstheorie Verw Gebiete . 52(3):309–319.
- Zaitsev, V. F. , Polyanin, A. D. (2002). Handbook of Exact Solutions for Ordinary Differential Equations . Boca Raton: CRC press.
- Abramowitz, M. , Stegun, I. A. (1964). Handbook of mathematical functions. With Formulas, Graphs, and Mathematical Tables , vol. 55. Washington, DC: Courier Corporation.
- Lebedev, N. N. , Silverman, R. A. (1972). Special Functions and Their Applications . London: Courier Corporation.
- Peters, G. W. , Shevchenko, P. V. (2015). Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk . Hoboken, NJ: John Wiley & Sons.
- Øksendal, B. (2003). Stochastic differential equations. In Stochastic Differential Equations . Springer: Berlin, pp. 65–84
- Lindelöf, E. (1894). Sur l’application de la méthode des approximations successives aux équations différentielles ordinaires du premier ordre. Comptes Rendus Hebdomadaires Des Séances de L’Académie Des Sciences . 116(3):454–457.
- Bingham, N. H. , Kiesel, R. (2013). Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives . London: Springer.