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.
Keywords: Viscosity solutions, Hamilton−Jacobi−Bellman equations, homogenization and singular perturbations, large deviations, stochastic volatility models
@article{COCV_2018__24_2_605_0, author = {Ghilli, Daria}, title = {Viscosity methods for large deviations estimates of multiscale stochastic processes}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {605--637}, publisher = {EDP-Sciences}, volume = {24}, number = {2}, year = {2018}, doi = {10.1051/cocv/2017051}, zbl = {1403.35334}, mrnumber = {3816407}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017051/} }
TY - JOUR AU - Ghilli, Daria TI - Viscosity methods for large deviations estimates of multiscale stochastic processes JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 605 EP - 637 VL - 24 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017051/ DO - 10.1051/cocv/2017051 LA - en ID - COCV_2018__24_2_605_0 ER -
%0 Journal Article %A Ghilli, Daria %T Viscosity methods for large deviations estimates of multiscale stochastic processes %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 605-637 %V 24 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017051/ %R 10.1051/cocv/2017051 %G en %F COCV_2018__24_2_605_0
Ghilli, Daria. Viscosity methods for large deviations estimates of multiscale stochastic processes. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 2, pp. 605-637. doi : 10.1051/cocv/2017051. http://archive.numdam.org/articles/10.1051/cocv/2017051/
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