On the Analysis of Ait-Sahalia-Type Model for Rough Volatility Modelling

Abstract

Fractional Brownian motion with Hurst parameter $$H<\frac{1}{2}$$ H < 1 2 is used widely, for instance, to describe ‘rough’ volatility data in finance. In this paper, we examine a generalised Ait-Sahalia-type model driven by a fractional Brownian motion with $$H<\frac{1}{2}$$ H < 1 2 and establish theoretical properties such as an existence-and-uniqueness theorem, regularity in the sense of Malliavin differentiability and higher moments of the strong solutions.

Malliavin Calculus and Its Application to Robust Optimal Investment for an Insider

“…For further work, since the quadratic BSDE corresponding to the robust optimal investment strategy for a large insider has no analytical solution at present, we could only resort to the numerical methods. Moreover, extending the optimization problem to other models, like the jump-diffusion model and the fractional Brownian motion model (see [49]), is also a subject of ongoing research.…”