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

2016/06/30 by Philippe G. LeFloch, LeFloch, Philippe G., Jean-Marc Mercier +1
Economics, Econometrics and Finance · Social Sciences · #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Numerical Analysis (math.NA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1606.09612

openalex publication_date 2016/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Polar factorization and monotone rearrangement of vector‐valued functions

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