[go: up one dir, main page]

IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v219y2024icp112-140.html
   My bibliography  Save this article

A monotone numerical integration method for mean–variance portfolio optimization under jump-diffusion models

Author

Listed:
  • Zhang, Hanwen
  • Dang, Duy-Minh
Abstract
We develop a highly efficient, easy-to-implement, and strictly monotone numerical integration method for Mean-Variance (MV) portfolio optimization. This method proves very efficient in realistic contexts, which involve jump-diffusion dynamics of the underlying controlled processes, discrete rebalancing, and the application of investment constraints, namely no-bankruptcy and leverage.

Suggested Citation

  • Zhang, Hanwen & Dang, Duy-Minh, 2024. "A monotone numerical integration method for mean–variance portfolio optimization under jump-diffusion models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 112-140.
  • Handle: RePEc:eee:matcom:v:219:y:2024:i:c:p:112-140
    DOI: 10.1016/j.matcom.2023.12.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423005189
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2023.12.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Michaud, Richard O. & Michaud, Robert O., 2008. "Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation," OUP Catalogue, Oxford University Press, edition 2, number 9780195331912.
    2. Wu, Huiling & Zeng, Yan, 2015. "Equilibrium investment strategy for defined-contribution pension schemes with generalized mean–variance criterion and mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 396-408.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. F. Cong & C. W. Oosterlee, 2017. "On Robust Multi-Period Pre-Commitment And Time-Consistent Mean-Variance Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-26, November.
    5. Elena Vigna, 2020. "On Time Consistency For Mean-Variance Portfolio Selection," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(06), pages 1-22, September.
    6. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    7. Francesco Menoncin & Elena Vigna, 2013. "Mean-variance target-based optimisation in DC plan with stochastic interest rate," Carlo Alberto Notebooks 337, Collegio Carlo Alberto.
    8. Wang, J. & Forsyth, P.A., 2011. "Continuous time mean variance asset allocation: A time-consistent strategy," European Journal of Operational Research, Elsevier, vol. 209(2), pages 184-201, March.
    9. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    10. Pieter M. Van Staden & Duy-Minh Dang & Peter A. Forsyth, 2021. "Practical Investment Consequences Of The Scalarization Parameter Formulation In Dynamic Mean–Variance Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(05), pages 1-49, August.
    11. Marc Romano & Nizar Touzi, 1997. "Contingent Claims and Market Completeness in a Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 399-412, October.
    12. Chen, Zhi-ping & Li, Gang & Guo, Ju-e, 2013. "Optimal investment policy in the time consistent mean–variance formulation," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 145-156.
    13. Liyuan Wang & Zhiping Chen, 2019. "Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion," Mathematics, MDPI, vol. 7(1), pages 1-16, January.
    14. Yoshiharu Sato, 2019. "Model-Free Reinforcement Learning for Financial Portfolios: A Brief Survey," Papers 1904.04973, arXiv.org, revised May 2019.
    15. Yao Tung Huang & Yue Kuen Kwok, 2016. "Regression-based Monte Carlo methods for stochastic control models: variable annuities with lifelong guarantees," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 905-928, June.
    16. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    17. Pavel V. Shevchenko & Xiaolin Luo, 2016. "A unified pricing of variable annuity guarantees under the optimal stochastic control framework," Papers 1605.00339, arXiv.org.
    18. Elena Vigna, 2014. "On efficiency of mean--variance based portfolio selection in defined contribution pension schemes," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 237-258, February.
    19. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    20. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    21. Dang, D.M. & Forsyth, P.A., 2016. "Better than pre-commitment mean-variance portfolio allocation strategies: A semi-self-financing Hamilton–Jacobi–Bellman equation approach," European Journal of Operational Research, Elsevier, vol. 250(3), pages 827-841.
    22. Van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2018. "Time-consistent mean–variance portfolio optimization: A numerical impulse control approach," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 9-28.
    23. Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 145-154, July.
    24. Tomas Björk & Agatha Murgoci, 2014. "A theory of Markovian time-inconsistent stochastic control in discrete time," Finance and Stochastics, Springer, vol. 18(3), pages 545-592, July.
    25. Liyuan Wang & Zhiping Chen, 2018. "Nash Equilibrium Strategy for a DC Pension Plan with State-Dependent Risk Aversion: A Multiperiod Mean-Variance Framework," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-17, October.
    26. Zhou, Zhongbao & Xiao, Helu & Yin, Jialing & Zeng, Ximei & Lin, Ling, 2016. "Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 187-202.
    27. Chendi Ni & Yuying Li & Peter Forsyth & Ray Carroll, 2022. "Optimal asset allocation for outperforming a stochastic benchmark target," Quantitative Finance, Taylor & Francis Journals, vol. 22(9), pages 1595-1626, September.
    28. Peter A. Forsyth & Kenneth R. Vetzal, 2017. "Dynamic mean variance asset allocation: Tests for robustness," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-37, June.
    29. Wei, Jiaqin & Wang, Tianxiao, 2017. "Time-consistent mean–variance asset–liability management with random coefficients," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 84-96.
    30. Xiang Lin & Yiping Qian, 2016. "Time-consistent mean-variance reinsurance-investment strategy for insurers under CEV model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(7), pages 646-671, August.
    31. Sun, Jingyun & Li, Zhongfei & Zeng, Yan, 2016. "Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump–diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 158-172.
    32. Cong, F. & Oosterlee, C.W., 2016. "On pre-commitment aspects of a time-consistent strategy for a mean-variance investor," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 178-193.
    33. Peter A. Forsyth & Kenneth R. Vetzal, 2019. "Optimal Asset Allocation for Retirement Saving: Deterministic Vs. Time Consistent Adaptive Strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(1), pages 1-37, January.
    34. Xiaolin Luo & Pavel V. Shevchenko, 2014. "Valuation of Variable Annuities with Guaranteed Minimum Withdrawal and Death Benefits via Stochastic Control Optimization," Papers 1411.5453, arXiv.org, revised Apr 2015.
    35. Li, Yuying & Forsyth, Peter A., 2019. "A data-driven neural network approach to optimal asset allocation for target based defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 189-204.
    36. Peter A. Forsyth & Kenneth R. Vetzal & Graham Westmacott, 2019. "Management of Portfolio Depletion Risk through Optimal Life Cycle Asset Allocation," North American Actuarial Journal, Taylor & Francis Journals, vol. 23(3), pages 447-468, July.
    37. van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2021. "The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors," European Journal of Operational Research, Elsevier, vol. 289(2), pages 774-792.
    38. Jennifer Alonso-García & Oliver Wood & Jonathan Ziveyi, 2018. "Pricing and hedging guaranteed minimum withdrawal benefits under a general Lévy framework using the COS method," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 1049-1075, June.
    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. Hanwen Zhang & Duy-Minh Dang, 2023. "A monotone numerical integration method for mean-variance portfolio optimization under jump-diffusion models," Papers 2309.05977, arXiv.org.
    2. van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2021. "The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors," European Journal of Operational Research, Elsevier, vol. 289(2), pages 774-792.
    3. Van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2018. "Time-consistent mean–variance portfolio optimization: A numerical impulse control approach," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 9-28.
    4. Pieter M. van Staden & Peter A. Forsyth & Yuying Li, 2023. "A parsimonious neural network approach to solve portfolio optimization problems without using dynamic programming," Papers 2303.08968, arXiv.org.
    5. Forsyth, Peter A., 2020. "Optimal dynamic asset allocation for DC plan accumulation/decumulation: Ambition-CVAR," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 230-245.
    6. Liyuan Wang & Zhiping Chen, 2019. "Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion," Mathematics, MDPI, vol. 7(1), pages 1-16, January.
    7. Bian, Lihua & Li, Zhongfei & Yao, Haixiang, 2018. "Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 78-94.
    8. Li, Yuying & Forsyth, Peter A., 2019. "A data-driven neural network approach to optimal asset allocation for target based defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 189-204.
    9. De Gennaro Aquino, Luca & Sornette, Didier & Strub, Moris S., 2023. "Portfolio selection with exploration of new investment assets," European Journal of Operational Research, Elsevier, vol. 310(2), pages 773-792.
    10. Chendi Ni & Yuying Li & Peter A. Forsyth, 2023. "Neural Network Approach to Portfolio Optimization with Leverage Constraints:a Case Study on High Inflation Investment," Papers 2304.05297, arXiv.org, revised May 2023.
    11. Bosserhoff, Frank & Stadje, Mitja, 2021. "Time-consistent mean-variance investment with unit linked life insurance contracts in a jump-diffusion setting," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 130-146.
    12. F. Cong & C. W. Oosterlee, 2017. "On Robust Multi-Period Pre-Commitment And Time-Consistent Mean-Variance Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-26, November.
    13. Li, Yongwu & Qiao, Han & Wang, Shouyang & Zhang, Ling, 2015. "Time-consistent investment strategy under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 187-197.
    14. Marc Chen & Mohammad Shirazi & Peter A. Forsyth & Yuying Li, 2023. "Machine Learning and Hamilton-Jacobi-Bellman Equation for Optimal Decumulation: a Comparison Study," Papers 2306.10582, arXiv.org.
    15. Cong, F. & Oosterlee, C.W., 2016. "On pre-commitment aspects of a time-consistent strategy for a mean-variance investor," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 178-193.
    16. Zhang, Jingong & Tan, Ken Seng & Weng, Chengguo, 2017. "Optimal hedging with basis risk under mean–variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 1-15.
    17. Peter A. Forsyth & Kenneth R. Vetzal, 2019. "Defined Contribution Pension Plans: Who Has Seen the Risk?," JRFM, MDPI, vol. 12(2), pages 1-27, April.
    18. Peter A. Forsyth & Kenneth R. Vetzal & G. Westmacott, 2022. "Optimal performance of a tontine overlay subject to withdrawal constraints," Papers 2211.10509, arXiv.org.
    19. Helu Xiao & Tiantian Ren & Yanfei Bai & Zhongbao Zhou, 2019. "Time-Consistent Investment-Reinsurance Strategies for the Insurer and the Reinsurer under the Generalized Mean-Variance Criteria," Mathematics, MDPI, vol. 7(9), pages 1-25, September.
    20. Sun, Jingyun & Li, Zhongfei & Zeng, Yan, 2016. "Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump–diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 158-172.

    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:eee:matcom:v:219:y:2024:i:c:p:112-140. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.