  We consider stochastic control systems affected by a fast mean reverting
volatility $Y(t)$ driven by a pure jump L\'evy process. Motivated by a large
literature on financial models, we assume that $Y(t)$ evolves at a faster time
scale $\frac{t}{\varepsilon}$ than the assets, and we study the asymptotics as
$\varepsilon\to 0$. This is a singular perturbation problem that we study
mostly by PDE methods within the theory of viscosity solutions.
