We construct a finite element like scheme for fully nonlinear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in finance. The schemes are monotone and robust. We prove that they converge in very general situations, including degenerate equations, multiple dimensions, relatively low regularity of the data, and for most (if not all) types of jump-models used in finance. In all cases we provide (probably optimal) error bounds. These bounds apply when grids are unstructured and integral terms are very singular, two features that are new or highly unusual in this setting.

A finite element like scheme for integro-partial differential Hamilton-Jacobi-Bellman equations / Camilli, Fabio; Jakobsen, E.. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - STAMPA. - 47:(2009), pp. 2407-2431. [10.1137/080723144]

A finite element like scheme for integro-partial differential Hamilton-Jacobi-Bellman equations

CAMILLI, FABIO;
2009

Abstract

We construct a finite element like scheme for fully nonlinear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in finance. The schemes are monotone and robust. We prove that they converge in very general situations, including degenerate equations, multiple dimensions, relatively low regularity of the data, and for most (if not all) types of jump-models used in finance. In all cases we provide (probably optimal) error bounds. These bounds apply when grids are unstructured and integral terms are very singular, two features that are new or highly unusual in this setting.
integro-partial differential equation; viscosity solution; numerical scheme; Levy process; error estimate
01 Pubblicazione su rivista::01a Articolo in rivista
A finite element like scheme for integro-partial differential Hamilton-Jacobi-Bellman equations / Camilli, Fabio; Jakobsen, E.. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - STAMPA. - 47:(2009), pp. 2407-2431. [10.1137/080723144]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/43948
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