English

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}
}
R2 v1 2026-06-23T17:30:15.350Z