# A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion models

arXiv: https://arxiv.org/abs/2401.06740 · HTML: https://mlsanity.com/paper/2401.06740/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 5 of its 32 references that are in the map.
- First posted on arXiv 12 Jan 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 5 of 5)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [The Deep Minimizing Movement Scheme](https://mlsanity.com/paper/2109.14851/) (2021)
- [A deep solver for BSDEs with jumps](https://mlsanity.com/paper/2211.04349/) (2022)

## Built on by (most cited first, 5 of 5)

- [Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs](https://mlsanity.com/paper/2405.05192/) (2024)
- [A time-stepping deep gradient flow method for option pricing in (rough) diffusion models](https://mlsanity.com/paper/2403.00746/) (2024)
- [Error Analysis of Deep PDE Solvers for Option Pricing](https://mlsanity.com/paper/2505.05121/) (2025)
- [Learning Geometric-Aware Quadrature Rules for Functional Minimization](https://mlsanity.com/paper/2508.05445/) (2025)
- [Convergence of the generalization error for deep gradient flow methods for PDEs](https://mlsanity.com/paper/2512.25017/) (2025)

## Abstract (arXiv)

We develop a novel deep learning approach for pricing European basket options written on assets that follow jump-diffusion dynamics. The option pricing problem is formulated as a partial integro-differential equation, which is approximated via a new implicit-explicit minimizing movement time-stepping approach, involving approximation by deep, residual-type Artificial Neural Networks (ANNs) for each time step. The integral operator is discretized via two different approaches: (a) a sparse-grid Gauss-Hermite approximation following localised coordinate axes arising from singular value decompositions, and (b) an ANN-based high-dimensional special-purpose quadrature rule. Crucially, the proposed ANN is constructed to ensure the appropriate asymptotic behavior of the solution for large values of the underlyings and also leads to consistent outputs with respect to a priori known qualitative properties of the solution. The performance and robustness with respect to the dimension of these methods are assessed in a series of numerical experiments involving the Merton jump-diffusion model, while a comparison with the deep Galerkin method and the deep BSDE solver with jumps further supports the merits of the proposed approach.