Geodesic
Convergence in multiscale financial models with non-Gaussian stochastic volatility
Bardi, Martino1  ; Cesaroni, Annalisa2  ; Scotti, Andrea3
1 Department of Mathematics, University of Padova, via Trieste 63, 35121 Padova, Italy
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
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 2, pp. 500-518

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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.

Reçu le :
DOI : 10.1051/cocv/2015015
Classification : 93C70, 49L25, 35R09, 91B28
Keywords: Singular perturbations, stochastic volatility, jump processes, viscosity solutions, Hamilton–Jacobi–Bellman equations, portfolio optimization

Bardi, Martino 1 ; Cesaroni, Annalisa 2 ; Scotti, Andrea 3

1 Department of Mathematics, University of Padova, via Trieste 63, 35121 Padova, Italy
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 
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     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},
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Bardi, Martino; Cesaroni, Annalisa; Scotti, Andrea. Convergence in multiscale financial models with non-Gaussian stochastic volatility. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 2, pp. 500-518. doi: 10.1051/cocv/2015015

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