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Dynamic Programming for controlled Markov families: abstractly and over Martingale Measures

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  • Gordan Zitkovic

Abstract

We describe an abstract control-theoretic framework in which the validity of the dynamic programming principle can be established in continuous time by a verification of a small number of structural properties. As an application we treat several cases of interest, most notably the lower-hedging and utility-maximization problems of financial mathematics both of which are naturally posed over ``sets of martingale measures''.

Suggested Citation

  • Gordan Zitkovic, 2013. "Dynamic Programming for controlled Markov families: abstractly and over Martingale Measures," Papers 1307.5163, arXiv.org, revised Mar 2014.
    • Handle: RePEc:arx:papers:1307.5163
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    References listed on IDEAS

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    1. Nutz, Marcel & van Handel, Ramon, 2013. "Constructing sublinear expectations on path space," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3100-3121.
    2. Jaksa Cvitanić & Walter Schachermayer & Hui Wang, 2017. "Erratum to: Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 21(3), pages 867-872, July.
    3. Steven E. Shreve & Dimitri P. Bertsekas, 1979. "Universally Measurable Policies in Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 15-30, February.
    4. Marcel Nutz & Ramon van Handel, 2012. "Constructing Sublinear Expectations on Path Space," Papers 1205.2415, arXiv.org, revised Apr 2013.
    5. Bruno Bouchard & Marcel Nutz, 2011. "Weak Dynamic Programming for Generalized State Constraints," Papers 1105.0745, arXiv.org, revised Oct 2012.
    6. Marcel Nutz, 2010. "Random G-expectations," Papers 1009.2168, arXiv.org, revised Sep 2013.
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    Cited by:

    1. Kexin Chen & Hoi Ying Wong, 2022. "Duality in optimal consumption--investment problems with alternative data," Papers 2210.08422, arXiv.org, revised Jul 2023.
    2. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.

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