Inserted: 27 may 2014
Last Updated: 18 apr 2016
Journal: ESAIM Control Optim. Calc. Var.
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