EXISTENCE AND UNIQUENESS OF SOLUTION FOR GENERALIZATION OF FRACTIONAL BESSEL TYPE PROCESS

Vũ Thị Hương

doi:10.34238/tnu-jst.2020.02.2203

EXISTENCE AND UNIQUENESS OF SOLUTION FOR GENERALIZATION OF FRACTIONAL BESSEL TYPE PROCESS

About this article

Received: 12/10/19 Revised: 18/02/20 Published: 26/02/20

Authors

Vu Thi Huong , University of Transport and Communications - Ha Noi - Vietnam

Abstract

The real financial models such as the short term interest rates, the log-volatility in Heston model are very well modeled by a fractional Brownian motion. This fact raises a question of developing a fractional generalization of the classical processes such as Cox - Ingersoll - Ross process, Bessel process. In this paper, we are interested in the fractional Bessel process (Mishura, Yurchenko-Tytarenko, 2018). More precisely, we consider a generalization of the fractional Bessel type process. We prove that the equation has a unique positive solution. Moreover, we study the supremum norm of the solution.

Keywords

Fractional stochastic differential equation; Fractional Brownian motion; Fractional Bessel process; Fractional Cox- Ingersoll- Ross process; Supremum norm.

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References

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DOI: https://doi.org/10.34238/tnu-jst.2020.02.2203

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