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- Title
Uniqueness in Cauchy problems for diffusive real-valued strict local martingales.
- Authors
Çetin, Umut; Larsen, Kasper
- 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 \frac 12-Hölder 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.
- Subjects
MARTINGALES (Mathematics); SMOOTHNESS of functions; SET functions; CAUCHY problem; BOUNDARY layer (Aerodynamics)
- Publication
Transactions of the American Mathematical Society, Series B, 2023, Vol 10, p381
- ISSN
2330-0000
- Publication type
Article
- DOI
10.1090/btran/141