Uniqueness in Cauchy problems for diffusive real-valued strict local martingales
Mathematical Finance
2022-05-11 v2
Abstract
For a real-valued one dimensional diffusive strict local martingale,, we provide a set of smooth functions in which the Cauchy problem has a unique classical solution under a local H\"older condition. Under the weaker Engelbert-Schmidt conditions, we provide a set in which the Cauchy problem has a unique weak solution. We exemplify our results using quadratic normal volatility models and the two dimensional Bessel process.
Cite
@article{arxiv.2007.15041,
title = {Uniqueness in Cauchy problems for diffusive real-valued strict local martingales},
author = {Umut Cetin and Kasper Larsen},
journal= {arXiv preprint arXiv:2007.15041},
year = {2022}
}