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Analytic solutions for infinite horizon stochastic optimal control problems via finite horizon approximation: A practical guide

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  • Ewald, Christian-Oliver
  • Wang, Wen-Kai

Abstract

We show how infinite horizon stochastic optimal control problems can be solved via studying their finite horizon approximations. This often leads to analytical solutions for the infinite horizon problem by studying phase diagrams, even in cases where the complexity of the finite horizon case does not permit analytic solutions. Our approach can be applied to many problems in dynamic economics.

Suggested Citation

  • Ewald, Christian-Oliver & Wang, Wen-Kai, 2011. "Analytic solutions for infinite horizon stochastic optimal control problems via finite horizon approximation: A practical guide," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 146-151, May.
  • Handle: RePEc:eee:matsoc:v:61:y:2011:i:3:p:146-151
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    References listed on IDEAS

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    1. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947, December.
    2. Fershtman, Chaim & Nitzan, Shmuel, 1991. "Dynamic voluntary provision of public goods," European Economic Review, Elsevier, vol. 35(5), pages 1057-1067, July.
    3. Athanassoglou, Stergios, 2010. "Dynamic nonpoint-source pollution control policy: Ambient transfers and uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2494-2509, December.
    4. Wang, Wen-Kai & Ewald, Christian-Oliver, 2010. "A stochastic differential Fishery game for a two species fish population with ecological interaction," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 844-857, May.
    5. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, December.
    6. Wen-Kai Wang & Christian-Oliver Ewald, 2010. "Dynamic voluntary provision of public goods with uncertainty: a stochastic differential game model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(2), pages 97-116, November.
    7. Athanassoglou, Stergios, 2009. "The Effect of Uncertainty on Pollution Control Policy," MPRA Paper 16898, University Library of Munich, Germany.
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    Cited by:

    1. Forster, Martin & La Torre, Davide & Lambert, Peter J., 2014. "Optimal control of inequality under uncertainty," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 53-59.
    2. Wen-Kai Wang & Christian-Oliver Ewald, 2010. "Dynamic voluntary provision of public goods with uncertainty: a stochastic differential game model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(2), pages 97-116, November.
    3. Wang, Wen-Kai & Ewald, Christian-Oliver, 2010. "A stochastic differential Fishery game for a two species fish population with ecological interaction," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 844-857, May.

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