Convergence in Multiscale Financial Models with Non-Gaussian Stochastic Volatility

Abstract

We consider stochastic control systems affected by a fast mean reverting volatility $Y(t)$ driven by a pure jump Lévy process. Motivated by a large literature on financial models, we assume that $Y(t)$ evolves at a faster time scale $\frac{t}{\epsilon }$ than the assets, and we study the asymptotics as $\epsilon \to 0$. This is a singular perturbation problem that we study mostly by PDE methods within the theory of viscosity solutions.

References in corpus (2)

• Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited
• Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications