Variational analysis for options with stochastic volatility and multiple factors

Joseph Frédéric Bonnans 1 Axel Kröner 2, 1
1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
Abstract : This paper performs a variational analysis for a class of Euro-pean or American options with stochastic volatility models, including those of Heston and Achdou-Tchou. Taking into account partial correlations and the presence of multiple factors, we obtain the well-posedness of the related partial differential equations, in some weigthed Sobolev spaces. This involves a generalization of the commutator analysis introduced by Achdou and Tchou in [2].
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Joseph Frédéric Bonnans, Axel Kröner. Variational analysis for options with stochastic volatility and multiple factors. SIAM Journal on Financial Mathematics, SIAM, 2018, 9 (2), pp.465-492. ⟨hal-01516011v3⟩

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