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Stochastic optimal multi-modes switching with a viscosity solution approach

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  • El Asri, Brahim
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    Abstract

    We consider the problem of optimal multi-modes switching in finite horizon, when the state of the system, including the switching cost functions are arbitrary (gij(t,x)≥0). We show existence of the optimal strategy, via a verification theorem. Finally, when the state of the system is a Markov process, we show that the vector of value functions of the optimal problem is the unique viscosity solution to the system of m variational partial differential inequalities with inter-connected obstacles.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 123 (2013)
    Issue (Month): 2 ()
    Pages: 579-602

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    Handle: RePEc:eee:spapps:v:123:y:2013:i:2:p:579-602

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    Related research

    Keywords: Real options; Backward stochastic differential equations; Snell envelope; Stopping times; Switching; Viscosity solution of PDEs; Variational inequalities;

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    1. Dixit, A., 1988. "Entry And Exit Decisions Under Uncertainty," Papers 91, Princeton, Department of Economics - Financial Research Center.
    2. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
    3. Rene Carmona & Michael Ludkovski, 2008. "Pricing Asset Scheduling Flexibility using Optimal Switching," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 405-447.
    4. 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.
    5. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-57, April.
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