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

Umut Cetin and Kasper Larsen

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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.

Date: 2020-07, Revised 2022-05
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2007.15041

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