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

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.