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Stochastic optimal multi-modes switching with a viscosity solution approach

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  • El Asri, Brahim

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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  • El Asri, Brahim, 2013. "Stochastic optimal multi-modes switching with a viscosity solution approach," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 579-602.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:2:p:579-602
    DOI: 10.1016/j.spa.2012.09.007
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    1. 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.
    2. Dixit, Avinash K, 1989. "Entry and Exit Decisions under Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 620-638, June.
    3. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    4. 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.
    5. 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.
    6. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    7. 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.
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    Cited by:

    1. Kiyoshi Suzuki, 2021. "Infinite-Horizon Optimal Switching Regions for a Pair-Trading Strategy with Quadratic Risk Aversion Considering Simultaneous Multiple Switchings: A Viscosity Solution Approach," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 336-360, February.

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