Uniqueness in cauchy problems for diffusive real-valued strict local martingales

Umut Çetin and Kasper Larsen

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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 1 2 \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.

Keywords: boundary layer; Cauchy problem; strict local martingales; Sturm-Liouville ODEs (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 26 pages
Date: 2023-03-06
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Transactions of the American Mathematical Society Series B, 6, March, 2023, 10(13), pp. 381-406. ISSN: 2330-0000

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:118743

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