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An approximation scheme for semilinear parabolic PDEs with convex and coercive Hamiltonians
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Huang, Shuo, Liang, Gechun and Zariphopoulou, Thaleia (2020) An approximation scheme for semilinear parabolic PDEs with convex and coercive Hamiltonians. SIAM Journal on Control and Optimization, 58 (1). pp. 165-191. doi:10.1137/18M1198831 ISSN 0363-0129.
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Official URL: http://dx.doi.org/10.1137/18M1198831
Abstract
We propose an approximation scheme for a class of semilinear parabolic equations that are convex and coercive in their gradients. Such equations arise often in pricing and portfolio management in incomplete markets and, more broadly, are directly connected to the representation of solutions to backward stochastic differential equations. The proposed scheme is based on splitting the equation into two parts, the first corresponding to a linear parabolic equation and the second to a Hamilton--Jacobi equation. The solutions of these two equations are approximated using, respectively, the Feynman--Kac and the Hopf--Lax formula. We establish the convergence of the scheme and determine the convergence rate, combining Krylov's shaking coefficients technique and the Barles--Jakobsen optimal switching approximation.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Differential equations, Parabolic -- Numerical solutions, Numerical analysis, Hilbert space, Differential equations, Hyperbolic, Hamiltonian operator | ||||||||||||
Journal or Publication Title: | SIAM Journal on Control and Optimization | ||||||||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||||||||
ISSN: | 0363-0129 | ||||||||||||
Official Date: | 9 January 2020 | ||||||||||||
Dates: |
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Volume: | 58 | ||||||||||||
Number: | 1 | ||||||||||||
Page Range: | pp. 165-191 | ||||||||||||
DOI: | 10.1137/18M1198831 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Copyright Holders: | © 2020, Society for Industrial and Applied Mathematics | ||||||||||||
Date of first compliant deposit: | 15 January 2020 | ||||||||||||
Date of first compliant Open Access: | 27 January 2020 | ||||||||||||
RIOXX Funder/Project Grant: |
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