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Strict local martingales and the Khasminskii test for explosions

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  • Dandapani, Aditi
  • Protter, Philip

Abstract

We exhibit sufficient conditions such that components of a multidimensional SDE giving rise to a local martingale M are strict local martingales or martingales. We assume that the equations have diffusion coefficients of the form σ(Mt,vt), with vt being a stochastic volatility term.

Suggested Citation

  • Dandapani, Aditi & Protter, Philip, 2022. "Strict local martingales and the Khasminskii test for explosions," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 716-728.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:716-728
    DOI: 10.1016/j.spa.2019.03.009
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    References listed on IDEAS

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    1. Hardy Hulley, 2010. "The Economic Plausibility of Strict Local Martingales in Financial Modelling," Research Paper Series 279, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
    3. Francesca Biagini & Hans Föllmer & Sorin Nedelcu, 2014. "Shifting martingale measures and the birth of a bubble as a submartingale," Finance and Stochastics, Springer, vol. 18(2), pages 297-326, April.
    4. Freddy Delbaen & Walter Schachermayer, 1998. "A Simple Counterexample to Several Problems in the Theory of Asset Pricing," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 1-11, January.
    5. Carole Bernard & Zhenyu Cui & Don McLeish, 2017. "On The Martingale Property In Stochastic Volatility Models Based On Time-Homogeneous Diffusions," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 194-223, January.
    6. David Criens, 2018. "Deterministic Criteria For The Absence And Existence Of Arbitrage In Multi-Dimensional Diffusion Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-41, February.
    7. Li, Xue-Mei, 2017. "Strict local martingales: Examples," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 65-68.
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