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 $t/\u03f5$ than the assets, and we study the asymptotics as $\u03f5\to 0$. This is a singular perturbation problem that we study mostly by PDE methods within the theory of viscosity solutions.

DOI: 10.1051/cocv/2015015

Keywords: Singular perturbations, stochastic volatility, jump processes, viscosity solutions, Hamilton–Jacobi–Bellman equations, portfolio optimization

^{1}; Cesaroni, Annalisa

^{2}; Scotti, Andrea

^{3}

@article{COCV_2016__22_2_500_0, author = {Bardi, Martino and Cesaroni, Annalisa and Scotti, Andrea}, title = {Convergence in multiscale financial models with {non-Gaussian} stochastic volatility}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {500--518}, publisher = {EDP-Sciences}, volume = {22}, number = {2}, year = {2016}, doi = {10.1051/cocv/2015015}, zbl = {1369.93713}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2015015/} }

TY - JOUR AU - Bardi, Martino AU - Cesaroni, Annalisa AU - Scotti, Andrea TI - Convergence in multiscale financial models with non-Gaussian stochastic volatility JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 500 EP - 518 VL - 22 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2015015/ DO - 10.1051/cocv/2015015 LA - en ID - COCV_2016__22_2_500_0 ER -

%0 Journal Article %A Bardi, Martino %A Cesaroni, Annalisa %A Scotti, Andrea %T Convergence in multiscale financial models with non-Gaussian stochastic volatility %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 500-518 %V 22 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2015015/ %R 10.1051/cocv/2015015 %G en %F COCV_2016__22_2_500_0

Bardi, Martino; Cesaroni, Annalisa; Scotti, Andrea. Convergence in multiscale financial models with non-Gaussian stochastic volatility. ESAIM: Control, Optimisation and Calculus of Variations, Volume 22 (2016) no. 2, pp. 500-518. doi : 10.1051/cocv/2015015. http://archive.numdam.org/articles/10.1051/cocv/2015015/

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