English

One-dimensional game-theoretic differential equations

Probability 2022-01-19 v1 Mathematical Finance

Abstract

We provide a very brief introduction to typical paths and the corresponding It\^o type integration. Relying on this robust It\^o integration, we prove an existence and uniqueness result for one-dimensional differential equations driven by typical paths with non-Lipschitz continuous coefficients in the spirit of Yamada--Watanabe as well as an approximation result in the spirit of Doss--Sussmann.

Cite

@article{arxiv.2101.08041,
  title  = {One-dimensional game-theoretic differential equations},
  author = {Rafał M. Łochowski and Nicolas Perkowski and David J. Prömel},
  journal= {arXiv preprint arXiv:2101.08041},
  year   = {2022}
}
R2 v1 2026-06-23T22:20:42.967Z