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}
}