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Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to Finance

Author

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  • N. C. Framstad

    (University of Oslo)

  • B. Øksendal

    (University of Oslo
    Norwegian School of Economics and Business Administration)

  • A. Sulem

    (INRIA, Domaine de Voluceau)

Abstract

We give a verification theorem by employing Arrow's generalization of the Mangasarian sufficient condition to a general jump diffusion setting and show the connections of adjoint processes to dynamic programming. The result is applied to financial optimization problems.

Suggested Citation

  • N. C. Framstad & B. Øksendal & A. Sulem, 2004. "Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to Finance," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 77-98, April.
    • Handle: RePEc:spr:joptap:v:121:y:2004:i:1:d:10.1023_b:jota.0000026132.62934.96
    DOI: 10.1023/B:JOTA.0000026132.62934.96
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    References listed on IDEAS

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    1. Rong, Situ, 1997. "On solutions of backward stochastic differential equations with jumps and applications," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 209-236, March.
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    Cited by:

    1. Calisto Guambe & Rodwell Kufakunesu & Gusti Van Zyl & Conrad Beyers, 2018. "Optimal asset allocation for a DC plan with partial information under inflation and mortality risks," Papers 1808.06337, arXiv.org, revised Aug 2018.
    2. 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.
    3. Zhongyang Sun & Junyi Guo & Xin Zhang, 2018. "Maximum Principle for Markov Regime-Switching Forward–Backward Stochastic Control System with Jumps and Relation to Dynamic Programming," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 319-350, February.
    4. Guo, Xin & Pham, Huyên & Wei, Xiaoli, 2023. "Itô’s formula for flows of measures on semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 350-390.
    5. Yang Shen & Bin Zou, 2021. "Mean-Variance Portfolio Selection in Contagious Markets," Papers 2110.09417, arXiv.org.
    6. Ruan, Xinfeng & Zhu, Wenli & Hu, Jin & Huang, Jiexiang, 2014. "Errata corrige optimal portfolio and consumption with habit formation in a jump diffusion market," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 235-236.
    7. Davide Torre & Danilo Liuzzi & Simone Marsiglio, 2017. "Pollution Control Under Uncertainty and Sustainability Concern," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 67(4), pages 885-903, August.
    8. Rodwell Kufakunesu & Calisto Guambe, 2018. "On the optimal investment-consumption and life insurance selection problem with an external stochastic factor," Papers 1808.04608, arXiv.org.
    9. Olivier Menoukeu Pamen, 2017. "Maximum Principles of Markov Regime-Switching Forward–Backward Stochastic Differential Equations with Jumps and Partial Information," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 373-410, November.
    10. Lesedi Mabitsela & Calisto Guambe & Rodwell Kufakunesu, 2018. "A note on representation of BSDE-based dynamic risk measures and dynamic capital allocations," Papers 1808.04611, arXiv.org.
    11. Yuchao Dong & Qingxin Meng, 2019. "Second-Order Necessary Conditions for Optimal Control with Recursive Utilities," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 494-524, August.
    12. T. T. K. An & B. Øksendal, 2008. "Maximum Principle for Stochastic Differential Games with Partial Information," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 463-483, December.
    13. Engel John C. Dela Vega & Robert J. Elliott, 2021. "A stochastic control approach to bid-ask price modelling," Papers 2112.02368, arXiv.org.

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