# An approximation scheme for semilinear parabolic PDEs with convex and coercive Hamiltonians

arXiv: https://arxiv.org/abs/1801.00583 · HTML: https://mlsanity.com/paper/1801.00583/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2018.

## Built on by (most cited first, 1 of 1)

- [A deep branching solver for fully nonlinear partial differential equations](https://mlsanity.com/paper/2203.03234/) (2022)

## Abstract (arXiv)

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 in 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 formulae. We establish the convergence of the scheme and determine the convergence rate, combining Krylov's shaking coefficients technique and Barles-Jakobsen's optimal switching approximation.