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Lévy processes

In: Non-Gaussian Merton-Black-Scholes Theory

Author

Listed:
  • Svetlana I. Boyarchenko

    (University of Texas at Austin, USA)

  • Sergei Z. Levendorskiĭ

    (Rostov State University of Economics, Russia)

Abstract

The following sections are included:Basic notation and definitionsRandom variablesConditional expectationThe Fourier transform and the Laplace transform. Characteristic functionsLévy processes: general definitionsLévy processes and infinitely divisible distributionsThe Lévy-Khintchine formula and generating tripletConstructions of Lévy processesExplicit constructionsSubordinators and subordinated processesLinear transformations of Lévy processesThe Wiener-Hopf factorizationLévy processes as Markov processesMarkov property and Feller propertyStopping times and the strong Markov propertyResolvent operator and infinitesimal generatorDynkin's formulaDualityAbsolutely continuous resolventsOperators $P^q_B$Boundary value problems for the Black-Scholes-type equationBoundary problems for the stationary Black-Scholes type equationBoundary problems for the non-stationary Black-Scholes type equationCommentary

Suggested Citation

  • Svetlana I. Boyarchenko & Sergei Z. Levendorskiĭ, 2002. "Lévy processes," World Scientific Book Chapters, in: Non-Gaussian Merton-Black-Scholes Theory, chapter 2, pages 39-66, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812777485_0002
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    Cited by:

    1. Chen, Yu-Fu & Funke, Michael, 2010. "Global Warming And Extreme Events: Rethinking The Timing And Intensity Of Environmental Policy," SIRE Discussion Papers 2010-48, Scottish Institute for Research in Economics (SIRE).
    2. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Mitov, Ivan & Fabozzi, Frank J., 2011. "Time series analysis for financial market meltdowns," Journal of Banking & Finance, Elsevier, vol. 35(8), pages 1879-1891, August.
    3. Adam Misiorek & Rafal Weron, 2010. "Heavy-tailed distributions in VaR calculations," HSC Research Reports HSC/10/05, Hugo Steinhaus Center, Wroclaw University of Technology.
    4. Ole E. Barndorff-Nielsen & Neil Shephard, 2012. "Basics of Levy processes," Economics Papers 2012-W06, Economics Group, Nuffield College, University of Oxford.
    5. Szymon Borak & Adam Misiorek & Rafał Weron, 2010. "Models for Heavy-tailed Asset Returns," SFB 649 Discussion Papers SFB649DP2010-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Luis Alvarez & Teppo Rakkolainen, 2010. "Investment timing in presence of downside risk: a certainty equivalent characterization," Annals of Finance, Springer, vol. 6(3), pages 317-333, July.
    7. Flavia Barsotti, 2012. "Optimal Capital Structure with Endogenous Default and Volatility Risk," Working Papers - Mathematical Economics 2012-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    8. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "American options: the EPV pricing model," Annals of Finance, Springer, vol. 1(3), pages 267-292, August.
    9. Sergei Levendorskii, 2002. "Pseudo-diffusions and Quadratic term structure models," Papers cond-mat/0212249, arXiv.org, revised Apr 2004.
    10. Oleg Kudryavtsev & Sergei Levendorskiǐ, 2009. "Fast and accurate pricing of barrier options under Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 531-562, September.
    11. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).

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