Convergence in multiscale financial models with non-Gaussian stochastic volatility

Bardi, Martino; Cesaroni, Annalisa; Scotti, Andrea

ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 2, pp. 500-518.

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

Classification : 93C70, 49L25, 35R09, 91B28
Mots clés : Singular perturbations, stochastic volatility, jump processes, viscosity solutions, Hamilton–Jacobi–Bellman equations, portfolio optimization

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