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

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  • Umut Cetin
  • Kasper Larsen

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.

Suggested Citation

  • Umut Cetin & Kasper Larsen, 2020. "Uniqueness in Cauchy problems for diffusive real-valued strict local martingales," Papers 2007.15041, arXiv.org, revised May 2022.
    • Handle: RePEc:arx:papers:2007.15041
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    References listed on IDEAS

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