Tail distribution of the integrated Jacobi diffusion process

  • Nguyen Tien Dung
  • Trinh Nhu Quynh
Keywords: Jacobi process, Tail distribution, Malliavin calculus.

Abstract

In this paper, we study the distribution of the integrated Jacobi diffusion processes with Brownian noise and fractional Brownian noise. Based on techniques of Malliavin calculus, we develop a unified method to obtain explicit estimates for the tail distribution of these integrated diffusions.

References

E.A. Abderrahim, E.H. Mostafa, M.G.Z.E. Abidine, Optimality of reinsurance treaties under a mean-ruin probability criterion. Stat. Optim. Inf. Comput. Vol. 7, June 2019, pp 383-393.

D. Ackerer, D. Filipovic, S. Pulido, The Jacobi stochastic volatility model. Finance Stoch. 22 (2018), no. 3, 667-700.

F. Delbaen, H. Shirakawa, An interest rate model with upper and lower bounds. Asia Pac Fin Mark 9(3) (2002), 191-209.

D. Dufresne, The integrated square-root process. Working paper, 2001, University of Montreal.

N. T. Dung, Jacobi processes driven by fractional Brownian motion. Taiwanese J. Math. 18 (2014), no. 3, 835-848.

C. Gourieroux, J. Jasiak, Multivariate Jacobi process with application to smooth transitions. J Econ, 131(1-2) (2006), 475-505.

M.M. Hossain, Probability modeling of monthly maximum sustained wind speed in Bangladesh. Stat. Optim. Inf. Comput. Vol. 7, March 2019, pp 75-84.

F. De Jong, F. C. Drost, B. J. M. Werker, A jump-diffusion model for exchange rates in a target zone. Statistica Neerlandica, 55 (2001), 270-300.

A. Kaplun, Bounded short-rate models with Ehrenfest and Jacobi processes. Ph.D. thesis, Technical University of Dortmund, 2010.

S. Karlin, H. M. Taylor, A second course in stochastic processes. Academic Press, New York (1981).

M. Li, Derivatives pricing on integrated diffusion processes: a general perturbation approach. The Journal of Futures Markets, 35(6) (2015), 582-595.

D. Nualart, The Malliavin Calculus and Related Topics. 2nd edition, Springer 2006.

H. Sugita, On a characterization of the Sobolev spaces over an abstract Wiener space. J. Math. Kyoto Univ. 25 (1985), no. 4, 717-725.

N. Privault, Stochastic analysis in discrete and continuous settings with normal martingales. Lecture Notes in Mathematics, 1982. Springer-Verlag, Berlin, 2009.

M. Zahle, Integration with respect to fractal functions and stochastic calculus. Part I, Probab. Theory Related Fields 111 (1998), 333-374.

Published
2020-07-01
How to Cite
Dung , N. T., & Quynh, T. N. (2020). Tail distribution of the integrated Jacobi diffusion process. Statistics, Optimization & Information Computing, 8(3), 790-800. https://doi.org/10.19139/soic-2310-5070-760
Section
Research Articles