Multi-level Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities

Martin Hutzenthaler; Thomas Kruse

doi:10.1137/17m1157015

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arXiv · 1711.01080

Multi-level Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities

Martin Hutzenthaler·Thomas Kruse

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Abstract

Parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) have a wide range of applications. In particular, high-dimensional PDEs with gradient-dependent nonlinearities appear often in the state-of-the-art pricing and hedging of financial derivatives. In this article we prove that semilinear heat equations with gradient-dependent nonlinearities can be approximated under suitable assumptions with computational complexity that grows polynomially both in the dimension and the reciprocal of the accuracy.

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Martin Hutzenthaler, Thomas Kruse. 2017-11-03. Multi-level Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities. https://doi.org/10.1137/17m1157015

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