An algorithm (CoDeFi) for overcoming the curse of dimensionality in mathematical finance

TL;DR

The paper introduces CoDeFi, an algorithm designed to efficiently solve high-dimensional partial differential equations common in mathematical finance, effectively overcoming the curse of dimensionality and enabling robust computations in complex stochastic models.

Contribution

The paper presents a novel algorithm, CoDeFi, that addresses the curse of dimensionality in solving PDEs relevant to finance, applicable to high-dimensional stochastic problems.

Findings

Successfully solves PDEs in high dimensions

Applicable to Kolmogorov-type and Black-Scholes equations

Maintains robustness in large-dimensional problems

Abstract

We present an algorithm (CoDeFi) which overcomes the curse of dimensionality (CoD) in scientific computations and, especially, in mathematical finance (Fi). Our method applies a broad class of partial differential equations such as Kolmogorov-type equations and, for instance, the Black and Scholes equation. As a main feature, our algorithm allows one to solve partial differential equations in large dimensions and provides a general framework for stochastic problems. In insurance or finance applications, the number of dimensions corresponds to the number of risk sources and it is crucial to have a numerical method that remains robust and reliable in large dimensions.