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Optimal stopping in Levy models, for non-monotone discontinuous payoffs

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  • Boyarchenko, Svetlana
  • Levendorskii, Sergei

Abstract

We give short proofs of general theorems about optimal entry and exit problems in Levy models, when payoff streams may have discontinuities and be non-monotone. As applications, we consider exit and entry problems in the theory of real options, and an entry problem with an embedded option to exit.

Suggested Citation

  • Boyarchenko, Svetlana & Levendorskii, Sergei, 2010. "Optimal stopping in Levy models, for non-monotone discontinuous payoffs," MPRA Paper 27999, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:27999
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    File URL: https://mpra.ub.uni-muenchen.de/27999/1/MPRA_paper_27999.pdf
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    References listed on IDEAS

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    1. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "American options: the EPV pricing model," Annals of Finance, Springer, vol. 1(3), pages 267-292, August.
    2. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    3. Steven R. Grenadier, 2002. "Option Exercise Games: An Application to the Equilibrium Investment Strategies of Firms," The Review of Financial Studies, Society for Financial Studies, vol. 15(3), pages 691-721.
    4. Alexander Novikov & Albert Shiryaev, 2004. "On an Effective Solution of the Optimal Stopping Problem for Random Walks," Research Paper Series 131, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Alexander Novikov & Albert Shiryaev, 2006. "On a Solution of the Optimal Stopping Problem for Processes with Independent Increments," Research Paper Series 178, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Svetlana Boyarchenko & Sergei Levendorski&icaron;, 2007. "Practical Guide To Real Options In Discrete Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(1), pages 311-342, February.
    7. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, May.
    8. Svetlana Boyarchenko, 2004. "Irreversible Decisions and Record-Setting News Principles," American Economic Review, American Economic Association, vol. 94(3), pages 557-568, June.
    9. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    10. Svetlana Boyarchenko & Sergei Levendorskii, 2007. "Irreversible Decisions under Uncertainty," Studies in Economic Theory, Springer, number 978-3-540-73746-9, September.
    11. Boyarchenko Svetlana & Levendorskii Sergei Z, 2006. "General Option Exercise Rules, with Applications to Embedded Options and Monopolistic Expansion," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-53, June.
    12. Michael D. Whinston, 1988. "Exit with Multiplant Firms," RAND Journal of Economics, The RAND Corporation, vol. 19(4), pages 568-588, Winter.
    13. Kerry Back & Dirk Paulsen, 2009. "Open-Loop Equilibria and Perfect Competition in Option Exercise Games," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4531-4552, November.
    14. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
    15. Boyarchenko, Svetlana & Levendorskii, Sergei, 2008. "Exit problems in regime-switching models," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 180-206, January.
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    Cited by:

    1. Thijssen, Jacco J.J. & Huisman, Kuno J.M. & Kort, Peter M., 2012. "Symmetric equilibrium strategies in game theoretic real option models," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 219-225.
    2. Moreno Othón M., 2014. "Consumption of Durable Goods under Ambiguity," Working Papers 2014-02, Banco de México.
    3. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.

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    More about this item

    Keywords

    optimal stopping; Levy processes; non-monotone discontinuous payoffs;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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