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A reading guide for last passage times with financial applications in view

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  • Ashkan Nikeghbali
  • Eckhard Platen

Abstract

In this survey on last passage times, we propose a new viewpoint which provides a unified approach to many different results which appear in the mathematical finance literature and in the theory of stochastic processes. In particular, we are able to improve the assumptions under which some well-known results are usually stated. Moreover we give some new and detailed calculations for the computation of the distribution of some large classes of last passage times. We have kept in this survey only the aspects of the theory which we expect potentially to be relevant for financial applications. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Ashkan Nikeghbali & Eckhard Platen, 2013. "A reading guide for last passage times with financial applications in view," Finance and Stochastics, Springer, vol. 17(3), pages 615-640, July.
    • Handle: RePEc:spr:finsto:v:17:y:2013:i:3:p:615-640
    DOI: 10.1007/s00780-013-0207-6
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    References listed on IDEAS

    as
    1. Nikeghbali, Ashkan, 2006. "A class of remarkable submartingales," Stochastic Processes and their Applications, Elsevier, vol. 116(6), pages 917-938, June.
    2. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195, April.
    3. Madan, D. & Roynette, B. & Yor, Marc, 2008. "Option prices as probabilities," Finance Research Letters, Elsevier, vol. 5(2), pages 79-87, June.
    4. Platen, Eckhard, 2000. "A minimal financial market model," SFB 373 Discussion Papers 2000,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    6. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Ju-Yi Yen & Marc Yor, 2011. "Call Option Prices Based on Bessel Processes," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 329-347, June.
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    Citations

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    Cited by:

    1. Kardaras, Constantinos, 2014. "On the characterisation of honest times that avoid all stopping times," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 373-384.
    2. Claudio Fontana & Monique Jeanblanc & Shiqi Song, 2012. "On arbitrages arising from honest times," Papers 1207.1759, arXiv.org, revised Jul 2013.
    3. Libo Li, 2022. "Characterisation of Honest Times and Optional Semimartingales of Class- $$(\Sigma )$$ ( Σ )," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2145-2175, December.
    4. Anna Aksamit & Tahir Choulli & Jun Deng & Monique Jeanblanc, 2013. "Non-Arbitrage up to Random Horizon for Semimartingale Models," Papers 1310.1142, arXiv.org, revised Feb 2014.
    5. Claudio Fontana & Monique Jeanblanc & Shiqi Song, 2014. "On arbitrages arising with honest times," Finance and Stochastics, Springer, vol. 18(3), pages 515-543, July.

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    More about this item

    Keywords

    Last passage times; Class Σ ; Running maximum; 60G17; 62P05; C02; C10; G10;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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