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

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  • 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 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.

Suggested Citation

  • Çetin, Umut & Larsen, Kasper, 2023. "Uniqueness in cauchy problems for diffusive real-valued strict local martingales," LSE Research Online Documents on Economics 118743, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:118743
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    File URL: http://eprints.lse.ac.uk/118743/
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    References listed on IDEAS

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    11. Hardy Hulley & Johannes Ruf, 2019. "Weak Tail Conditions for Local Martingales," Published Paper Series 2019-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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    Cited by:

    1. Yukihiro Tsuzuki, 2024. "Boundary conditions at infinity for Black-Scholes equations," Papers 2401.05549, arXiv.org, revised Sep 2024.
    2. Ekaterina A. Ladykova & Olga S. Rozanova, 2025. "On non-uniqueness in the option valuation problem," Papers 2501.18721, arXiv.org.

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    More about this item

    Keywords

    boundary layer; Cauchy problem; strict local martingales; Sturm-Liouville ODEs;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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