Calculus of Variations and Geometric Measure Theory

M. Bardi - A. Cesaroni - A. Scotti

Convergence in Multiscale Financial Models with Non-Gaussian Stochastic Volatility

created by bardi on 27 May 2014
modified by cesaroni on 18 Apr 2016


Published Paper

Inserted: 27 may 2014
Last Updated: 18 apr 2016

Journal: ESAIM Control Optim. Calc. Var.
Volume: 22
Number: 2
Pages: 500-518
Year: 2016
Doi: 10.1051/cocv/2015015


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

Keywords: Viscosity solutions, singular perturbations, portfolio optimization, Hamilton-Jacobi-Bellman equations, jump processes, stochastic volatility