IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2508.01138.html
   My bibliography  Save this paper

Two Stochastic Control Methods for Mean-Variance Portfolio Selection of Jump Diffusions and Their Relationship

Author

Listed:
  • Qiyue Zhang
  • Jingtao Shi

Abstract

This paper is concerned with the maximum principle and dynamic programming principle for mean-variance portfolio selection of jump diffusions and their relationship. First, the optimal portfolio and efficient frontier of the problem are obtained using both methods. Furthermore, the relationship between these two methods is investigated. Specially, the connections between the adjoint processes and value function are given.

Suggested Citation

  • Qiyue Zhang & Jingtao Shi, 2025. "Two Stochastic Control Methods for Mean-Variance Portfolio Selection of Jump Diffusions and Their Relationship," Papers 2508.01138, arXiv.org.
    • Handle: RePEc:arx:papers:2508.01138
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2508.01138
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Wenjing Guo & Chengming Xu, 2004. "Optimal portfolio selection when stock prices follow an jump-diffusion process," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(3), pages 485-496, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Kuang, Daipeng & Li, Jianli & Gao, Dongdong & Luo, Danfeng, 2024. "Stochastic near-optimal control for a system with Markovian switching and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    5. 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.
    6. Wenjing Guo & Chengming Xu, 2007. "Correction on “Optimal portfolio selection when stock prices follow an jump-diffusion process”," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 559-564, June.
    7. Tian Chen & Hongyu Shi & Zhen Wu, 2025. "A Progressive Maximum Principle of Fully Coupled Mean-Field System with Jumps," Journal of Optimization Theory and Applications, Springer, vol. 206(3), pages 1-28, September.
    8. Ricardo Huamán-Aguilar & Abel Cadenillas, 2015. "Government Debt Control: Optimal Currency Portfolio and Payments," Operations Research, INFORMS, vol. 63(5), pages 1044-1057, October.
    9. 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.
    10. Josa-Fombellida, Ricardo & López-Casado, Paula, 2025. "Optimal investment and benefit strategies for a target benefit pension plan where the risky assets are jump diffusion processes," Insurance: Mathematics and Economics, Elsevier, vol. 121(C), pages 100-110.
    11. Moualkia, Seyfeddine & Liu, Yang & Qiu, Jianlong & Lu, Jianquan, 2024. "An averaging result for fractional variable-order neutral differential equations with variable delays driven by Markovian switching and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    12. 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.
    13. Huiling Wu, 2013. "Mean-Variance Portfolio Selection with a Stochastic Cash Flow in a Markov-switching Jump–Diffusion Market," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 918-934, September.
    14. Burcu Aydoğan & Mogens Steffensen, 2025. "Optimal investment strategies under the relative performance in jump-diffusion markets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 48(1), pages 179-204, June.
    15. 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.
    16. Zhongyang Sun & Xianping Guo, 2019. "Equilibrium for a Time-Inconsistent Stochastic Linear–Quadratic Control System with Jumps and Its Application to the Mean-Variance Problem," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 383-410, May.
    17. Engel John C. Dela Vega & Robert J. Elliott, 2021. "A stochastic control approach to bid-ask price modelling," Papers 2112.02368, arXiv.org.
    18. Yu Yang & Yonghong Wu & Benchawan Wiwatanapataphee, 2020. "Time-consistent mean–variance asset-liability management in a regime-switching jump-diffusion market," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(4), pages 401-427, December.
    19. Nicole Bäuerle & Ulrich Rieder, 2013. "Optimal Deterministic Investment Strategies for Insurers," Risks, MDPI, vol. 1(3), pages 1-18, November.
    20. Fikriye Yılmaz & Hacer Öz Bakan & Gerhard-Wilhelm Weber, 2024. "Weak Second-Order Conditions of Runge–Kutta Method for Stochastic Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 497-517, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2508.01138. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.