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 t/∈ than the assets, and we study the asymptotics as ∈ → 0. This is a singular perturbation problem that we study mostly by PDE methods within the theory of viscosity solutions.
Convergence in Multiscale Financial Models with Non-Gaussian Stochastic Volatility
BARDI, MARTINO;
2016
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 t/∈ than the assets, and we study the asymptotics as ∈ → 0. This is a singular perturbation problem that we study mostly by PDE methods within the theory of viscosity solutions.File in questo prodotto:
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