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The explicit solution to a sequential switching problem with non-smooth data

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Listed:
  • Johnson, Timothy C.
  • Zervos, Mihail

Abstract

We consider the problem faced by a decision maker who can switch between two random payoff flows. Each of these payoff flows is an additive functional of a general 1D Ito diffusion. There are no bounds on the number or on the frequency of the times at which the decision maker can switch, but each switching incurs a cost, which may depend on the underlying diffusion. The objective of the decision maker is to select a sequence of switching times that maximizes the associated expected discounted payoff flow. In this context, we develop and study a model in the presence of assumptions that involve minimal smoothness requirements from the running payoff and switching cost functions, but which guarantee that the optimal strategies have relatively simple forms. In particular, we derive a complete and explicit characterization of the decision maker's optimal tactics, which can take qualitatively different forms, depending on the problem data.

Suggested Citation

  • Johnson, Timothy C. & Zervos, Mihail, 2010. "The explicit solution to a sequential switching problem with non-smooth data," LSE Research Online Documents on Economics 29003, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:29003
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    File URL: http://eprints.lse.ac.uk/29003/
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    References listed on IDEAS

    as
    1. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
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    3. Boualem Djehiche & Said Hamadène, 2009. "On A Finite Horizon Starting And Stopping Problem With Risk Of Abandonment," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 523-543.
    4. Guo, Xin & Pham, Huyên, 2005. "Optimal partially reversible investment with entry decision and general production function," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 705-736, May.
    5. Said Hamadène & Monique Jeanblanc, 2007. "On the Starting and Stopping Problem: Application in Reversible Investments," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 182-192, February.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Pui Chan Lon & Mihail Zervos, 2011. "A Model for Optimally Advertising and Launching a Product," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 363-376, May.
    2. Mihail Zervos & Carlos Oliveira & Kate Duckworth, 2018. "An investment model with switching costs and the option to abandon," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 417-443, December.
    3. Korn, Ralf & Melnyk, Yaroslav & Seifried, Frank Thomas, 2017. "Stochastic impulse control with regime-switching dynamics," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1024-1042.

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    More about this item

    Keywords

    optimal switching; sequential entry and exit decisions; stochastic impulse control; system of variational inequalities; ISI;
    All these keywords.

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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