| Issue |
ESAIM: COCV
Volume 22, Number 2, April-June 2016
|
|
|---|---|---|
| Page(s) | 500 - 518 | |
| DOI | https://doi.org/10.1051/cocv/2015015 | |
| Published online | 10 March 2016 | |
Convergence in multiscale financial models with non-Gaussian stochastic volatility∗,∗∗
1
Department of Mathematics, University of Padova,
via Trieste 63, 35121
Padova,
Italy
bardi@math.unipd.it
2
Department of Mathematics, currently at Department of Statistical
Sciences, University of Padova, via
C. Battisti 241, 35121
Padova,
Italy
acesar@math.unipd.it
3
Department of Mathematics, current address Via Podgora 107, 30172, Mestre ( VE),
Italy
andrea.scotti4@gmail.com
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
© EDP Sciences, SMAI 2016
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