Parameter estimation in reflected Vasicek model: least-squares approach

Fateh Merahi; Abdelouahab Bibi

doi:10.5269/bspm.64536

Fateh Merahi Department of Mathematics, Batna 2 University, Batna , Algeria
Abdelouahab Bibi

Résumé

In this paper, we investigate least squares estimation (LSE) for continuou-time reflected Ornstein-Uhlenbeck (ROU) processes with one and two-sided barriers. So, we derive explicit formulas for the estimators, and then we prove their strong consistency and asymptotic normality. We also illustrate the asymptotic properties of the estimators through a simulation study.

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Références

Ata, B and Harrison, J.M and Shepp, L.A., Drift rate control of a Brownian processing system , Annals of Applied Probability 15, 1145-1160, (2005).

Yang, X and Ren, G and Wang, Y and Bo, L and Li, D., Modeling the exchange rate in a target zone by a reflected Ornstein-Uhlenbeck process, SSRN Electronic Journal, (2016).

Bo, L and Tang, D and Wang, Y and Yang, X., On the conditional default probability in a regulated market: a structural approach, Quantitative Finance 11, 1695-1702, (2011).

Bo, L and Wang, Y and Yang, X., Some integral functionals of reflected SDEs and their applications in finance , Quantitative Finance 11 , 343-348, (2010).

Bo, L and Wang, Y and Yang, X and Zhang, G., Maximum likelihood estimation for reflected Ornstein-Uhlenbeck processes, Journal of Statistical Planning and Inference 141, 588-596, (2011).

Bo, L and Zhang, L and Wang, Y., On the first passage times of reflected O-U processes with two-sided barriers, Queueing Systems 54, 313-316, (2006).

Glasserman, P., Monte Carlo Methods in Financial Engineering, Springer, New York, (2004).

Harrison, M., Brownian Motion and Stochastic Flow Systems, John Wiley Sons, NewYork, (1986).

Linetsky, V., On the transition densities for reflected diffusion, Adv. in Appl. Probab. 37, 435-460, (2005).

Hu, Y and Lee, C and Lee, M and Song, J., Parameter estimation for reflected Ornstein-Uhlenbeck processes with discrete observations, Statistical Inference for Stochastic, 18(3), 279-291, (2015).

Kallenberg, O., Fandtation of Modern Probability, Springer-Verlagn, New York, (1997).

Krugman, P.R., Target zones and exchange rate dynamics, Quarterly Journal of Economics 106, 669-682, (1991).

Lee, C and Bishwal, J.P.N and Lee, M.H., Sequential maximum likelihood estimation for reflected Ornstein-Uhlenbeck processes, J. Statist. Plann. Inference 142, 1234-1242, (2012).

Lepingle, D., Euler scheme for reflected stochastic differential equations, Mathematics and Computers in Simulation 38,119-126, (1995).

Lions, P and Sznitman, A., Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. 17, 511-537, (1984).

Ricciardi, L.M., Stochastic population models II. Diffusion models, Lecture Note at the International School on Mathematical Ecology, (1985).

Ricciardi, L M and Sacerdote, L., On the probability densities of an Ornstein-Uhlenbeck process with a reflecting boundary, Journal of Applied Probability 24, 355-369, (1987).

Prakasa Rao, B.L.S., Statistical Inference for Diffusion Type Processes, Arnold (Co-published by Oxford University Press), New York, , (1999).

Valdivieso, L and Schoutens, W and Tuerlinckx, F., Maximum likelihood estimation in processes of Ornstein-Uhlenbeck type, Statistical Inference for Stochastic Processes 12, 1-19, (2009).

Ward, A and Glynn, P., A diffusion approximation for Markovian queue with reneging, Queueing Systems 43,103-128, (2003).

Ward, A and Glynn, P., Properties of the reflected Ornstein-Uhlenbeck process, Queueing Systems 44, 109-123, (2003).

Whitt, W., Stochastic Process Limits. Springer Series in Operations Research, Springer-Verlag, New York, (2002).

Zhu, C., Some limiting results of reflected Ornstein-Uhlenbeck processes with two-sided barriers, Bull. Korean Math. Soc. Vol 54(2), 573-581, (2016).