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Optimal stopping made easy

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  • Boyarchenko, Svetlana
  • Levendorskii[caron], Sergei

Abstract

This paper presents a simple discrete time model for valuing real options. A short proof of optimal exercise rules for the standard problems in the real options theory is given in the binomial and trinomial models, and more generally, when the underlying uncertainty is modelled as a random walk on a lattice. The method of the paper is based on the use of the expected present value operators. With straightforward modifications, the method works in discrete time--continuous space, continuous time--continuous space and continuous time--discrete space models.
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  • Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
  • Handle: RePEc:eee:mateco:v:43:y:2007:i:2:p:201-217
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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.
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    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. Svetlana Boyarchenko & Sergei Levendorskii, 2004. "Real options and the universal bad news principle," Finance 0405011, University Library of Munich, Germany.
    10. 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 1-51, June.
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    Cited by:

    1. Mohammad Hossein Dehghani, 2014. "Strategic Technology Adoption under Technological Uncertainty," Iranian Economic Review (IER), Faculty of Economics,University of Tehran.Tehran,Iran, vol. 18(1), pages 1-31, Winter.
    2. Luis Alvarez & Teppo Rakkolainen, 2009. "Optimal payout policy in presence of downside risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 27-58, March.
    3. Abbring, J.H., 2009. "Mixed Hitting-Time Models," Other publications TiSEM 6c745572-a041-4990-a767-6, Tilburg University, School of Economics and Management.
    4. Jaap H. Abbring, 0000. "Mixed Hitting-Time Models," Tinbergen Institute Discussion Papers 07-057/3, Tinbergen Institute, revised 11 Aug 2009.
    5. Sergei Levendorskiĭ, 2022. "Operators and Boundary Problems in Finance, Economics and Insurance: Peculiarities, Efficient Methods and Outstanding Problems," Mathematics, MDPI, vol. 10(7), pages 1-36, March.
    6. Moreno Othón M., 2014. "Consumption of Durable Goods under Ambiguity," Working Papers 2014-02, Banco de México.
    7. Jaap H. Abbring & Tim Salimans, 2019. "The Likelihood of Mixed Hitting Times," Papers 1905.03463, arXiv.org, revised Apr 2021.
    8. Jaap H. Abbring, 2012. "Mixed Hitting‐Time Models," Econometrica, Econometric Society, vol. 80(2), pages 783-819, March.
    9. GAHUNGU, Joachim & SMEERS, Yves, 2011. "Sufficient and necessary conditions for perpetual multi-assets exchange options," LIDAM Discussion Papers CORE 2011035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Luis H. R. Alvarez & Teppo A. Rakkolainen, 2006. "A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions," Discussion Papers 9, Aboa Centre for Economics.
    11. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.
    12. Abbring, Jaap H. & Salimans, Tim, 2021. "The likelihood of mixed hitting times," Journal of Econometrics, Elsevier, vol. 223(2), pages 361-375.
    13. Mitya Boyarchenko & Sergei Levendorskiĭ, 2009. "Prices And Sensitivities Of Barrier And First-Touch Digital Options In Lévy-Driven Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(08), pages 1125-1170.
    14. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "A theory of endogenous time preference, and discounted utility anomalies," Microeconomics 0506005, University Library of Munich, Germany.
    15. Yong-Chao Zhang, 2017. "Entry–Exit Decisions with Underlying Processes Following Geometric Lévy Processes," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 309-327, January.
    16. 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.
    17. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "Discount factors ex post and ex ante, and discounted utility anomalies," Microeconomics 0510013, University Library of Munich, Germany, revised 13 Dec 2005.
    18. Livdan, Dmitry & Nezlobin, Alexander, 2022. "Incentivizing irreversible investment," LSE Research Online Documents on Economics 110531, London School of Economics and Political Science, LSE Library.
    19. Fernando A. C. C. Fonte & Dalila B. M. M. Fontes, 2007. "Optimal investment timing using Markov jump price processes," FEP Working Papers 245, Universidade do Porto, Faculdade de Economia do Porto.
    20. Mitya Boyarchenko & Marco De Innocentis & Sergei Levendorskiĭ, 2011. "Prices Of Barrier And First-Touch Digital Options In Lévy-Driven Models, Near Barrier," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(07), pages 1045-1090.
    21. Boyarchenko, Svetlana & Levendorskii, Sergei, 2010. "Optimal stopping in Levy models, for non-monotone discontinuous payoffs," MPRA Paper 27999, University Library of Munich, Germany.
    22. Jaap H. Abbring, 2010. "Identification of Dynamic Discrete Choice Models," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 367-394, September.
    23. Relativo, Jona Princess & Sumayang, Mildred & Diasana, Sarah Jean & Murcia, John Vianne, 2016. "Capital Investment Decisions of Micro, Small and Medium Enterprises: The Case of Digos City," MPRA Paper 79574, University Library of Munich, Germany, revised 07 Jun 2017.
    24. Dehghani Mohammad H., 2014. "Policy Uncertainty and Technology Adoption," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 14(4), pages 1-26, October.

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    More about this item

    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
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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