Department of Mathematics, University of Padova,
via Trieste 63, 35121
2 Department of Mathematics, currently at Department of Statistical Sciences, University of Padova, via C. Battisti 241, 35121 Padova, Italy
3 Department of Mathematics, current address Via Podgora 107, 30172, Mestre ( VE), Italy
Received: 26 May 2014
Revised: 11 February 2015
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/ϵ than the assets, and we study the asymptotics as ϵ → 0. This is a singular perturbation problem that we study mostly by PDE methods within the theory of viscosity solutions.
Mathematics Subject Classification: 93C70 / 49L25 / 35R09 / 91B28
Key words: Singular perturbations / stochastic volatility / jump processes / viscosity solutions / Hamilton–Jacobi–Bellman equations / portfolio optimization
Partially supported by the Fondazione CaRiPaRo Project “Nonlinear Partial Differential Equations: models, analysis, and control-theoretic problems” and the European Project Marie Curie ITN “SADCO – Sensitivity Analysis for Deterministic Controller Design”.
© EDP Sciences, SMAI 2016