Analysis of the fractional Cox-Ingersoll-Ross model based on optimal stopping rules

In this paper, based on optimal stopping rules, we study the inverse problem of sequential inference of the unknown mean reversion parameters in the fractional Cox-Ingersoll-Ross model which has been the main building block for interest rate and stochastic volatility models.For forward problem, this type of observations are used in the pricing of American options.We observe the process both continuously and discretely in time.Continuous observation has theoretical interest and discrete observations have practical interest.We have a unified theory for the subcritical, critical and supercritical cases.We discuss several stopping rules based on barrier, threshold and observed Fisher information.We also consider processes with jumps and long-memory.