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On Infinite Horizon Optimal Stopping of General Random Walk


  • Jukka Lempa

    (Department of Economics, Quantitative Methods in Management, Turku School of Economics)


The objective of this study is to provide an alternative characterization of the optimal value function of a certain Black- Scholes-type optimal stopping problem where the underlying stochastic process is a general random walk, i.e. the process constituted by partial sums of an IID sequence of random variables. Furthermore, the pasting principle of this optimal stopping problem is studied.

Suggested Citation

  • Jukka Lempa, 2006. "On Infinite Horizon Optimal Stopping of General Random Walk," Discussion Papers 3, Aboa Centre for Economics.
  • Handle: RePEc:tkk:dpaper:dp3

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    References listed on IDEAS

    1. Luis H. R. Alvarez, 2001. "Reward functionals, salvage values, and optimal stopping," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(2), pages 315-337, December.
    2. 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.
    3. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487,
    4. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
    5. 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.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
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    Cited by:

    1. 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.

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    More about this item


    General random walk; optimal stopping; minimal functions; continuous pasting;
    All these keywords.

    JEL classification:

    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • Q23 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Forestry

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