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First Order BSPDEs in higher dimension for optimal control problems

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  • Nikolai Dokuchaev

Abstract

The paper studies the First Order BSPDEs (Backward Stochastic Partial Differential Equations) suggested earlier for a case of multidimensional state domain with a boundary. These equations represent analogs of Hamilton-Jacobi-Bellman equations and allow to construct the value function for stochastic optimal control problems with unspecified dynamics where the underlying processes do not necessarily satisfy stochastic differential equations of a known kind with a given structure. The problems considered arise in financial modelling.

Suggested Citation

  • Nikolai Dokuchaev, 2016. "First Order BSPDEs in higher dimension for optimal control problems," Papers 1603.06825, arXiv.org, revised Oct 2018.
    • Handle: RePEc:arx:papers:1603.06825
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    References listed on IDEAS

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    1. David B. Brown & James E. Smith & Peng Sun, 2010. "Information Relaxations and Duality in Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 58(4-part-1), pages 785-801, August.
    2. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    3. Christian Bender, 2011. "Dual pricing of multi-exercise options under volume constraints," Finance and Stochastics, Springer, vol. 15(1), pages 1-26, January.
    4. Christian Bender & Nikolai Dokuchaev, 2013. "A First-Order BSPDE for Swing Option Pricing," Papers 1305.3988, arXiv.org.
    5. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
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