Viscosity methods for large deviations estimates of multiscale stochastic processes

Daria Ghilli, Karl-Franzens University of Graz, Universitatplatz 3, Austria

^a Corresponding author: daria.ghilli@uni-graz.at

Received: 16 May 2016
Revised: 3 July 2017
Accepted: 21 July 2017

Abstract

We study singular perturbation problems for second order HJB equations in an unbounded setting. The main applications are large deviations estimates for the short maturity asymptotics of stochastic systems affected by a stochastic volatility, where the volatility is modelled by a process evolving at a faster time scale and satisfying some condition implying ergodicity.