IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2108.09985.html
   My bibliography  Save this paper

Continuous-time Portfolio Optimization for Absolute Return Funds

Author

Listed:
  • Masashi Ieda

Abstract

This paper investigates a continuous-time portfolio optimization problem with the following features: (i) a no-short selling constraint; (ii) a leverage constraint, that is, an upper limit for the sum of portfolio weights; and (iii) a performance criterion based on the lower mean square error between the investor's wealth and a predetermined target wealth level. Since the target level is defined by a deterministic function independent of market indices, it corresponds to the criterion of absolute return funds. The model is formulated using the stochastic control framework with explicit boundary conditions. The corresponding Hamilton-Jacobi-Bellman equation is solved numerically using the kernel-based collocation method. However, a straightforward implementation does not offer a stable and acceptable investment strategy; thus, some techniques to address this shortcoming are proposed. By applying the proposed methodology, two numerical results are obtained: one uses artificial data, and the other uses empirical data from Japanese organizations. There are two implications from the first result: how to stabilize the numerical solution, and a technique to circumvent the plummeting achievement rate close to the terminal time. The second result implies that leverage is inevitable to achieve the target level in the setting discussed in this paper.

Suggested Citation

  • Masashi Ieda, 2021. "Continuous-time Portfolio Optimization for Absolute Return Funds," Papers 2108.09985, arXiv.org, revised Mar 2022.
    • Handle: RePEc:arx:papers:2108.09985
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2108.09985
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Masashi Ieda & Takashi Yamashita & Yumiharu Nakano, 2013. "A liability tracking approach to long term management of pension funds," Papers 1303.3956, arXiv.org.
    2. Sundaresan, S.M., 2000. "Continuous-Time Methods in Finance: A Review and an Assessment," Papers 00-03, Columbia - Graduate School of Business.
    3. Hiroaki Hata & Jun Sekine, 2017. "Risk-Sensitive Asset Management in a Wishart-Autoregressive Factor Model with Jumps," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 24(3), pages 221-252, September.
    4. Guiyuan Ma & Song-Ping Zhu, 2019. "Optimal investment and consumption under a continuous-time cointegration model with exponential utility," Quantitative Finance, Taylor & Francis Journals, vol. 19(7), pages 1135-1149, July.
    5. Romuald Elie & Nizar Touzi, 2008. "Optimal lifetime consumption and investment under a drawdown constraint," Finance and Stochastics, Springer, vol. 12(3), pages 299-330, July.
    6. Huang, Dashan & Zhu, Shu-Shang & Fabozzi, Frank J. & Fukushima, Masao, 2008. "Portfolio selection with uncertain exit time: A robust CVaR approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 594-623, February.
    7. Panos Xidonas & Ralph Steuer & Christis Hassapis, 2020. "Robust portfolio optimization: a categorized bibliographic review," Annals of Operations Research, Springer, vol. 292(1), pages 533-552, September.
    8. J. Wang & P. A. Forsyth, 2012. "Comparison Of Mean Variance Like Strategies For Optimal Asset Allocation Problems," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-32.
    9. Christopher W. Miller & Insoon Yang, 2015. "Optimal Control of Conditional Value-at-Risk in Continuous Time," Papers 1512.05015, arXiv.org, revised Jan 2017.
    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. Masashi Ieda, 2022. "Continuous-Time Portfolio Optimization for Absolute Return Funds," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(4), pages 675-696, December.
    2. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.
    3. Long, Hongwei & Ma, Chunhua & Shimizu, Yasutaka, 2017. "Least squares estimators for stochastic differential equations driven by small Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1475-1495.
    4. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, August.
    5. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2020. "Optimal ratcheting of dividends in a Brownian risk model," Papers 2012.10632, arXiv.org.
    6. Carré, Sylvain & Cohen, Daniel & Villemot, Sébastien, 2019. "The sources of sovereign risk: a calibration based on Lévy stochastic processes," Journal of International Economics, Elsevier, vol. 118(C), pages 31-43.
    7. Di Giacinto, Marina & Federico, Salvatore & Gozzi, Fausto & Vigna, Elena, 2014. "Income drawdown option with minimum guarantee," European Journal of Operational Research, Elsevier, vol. 234(3), pages 610-624.
    8. Constantinos Kardaras & Jan Obłój & Eckhard Platen, 2017. "The Numéraire Property And Long-Term Growth Optimality For Drawdown-Constrained Investments," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 68-95, January.
    9. Palacios Huerta, Ignacio & Pérez Kakabadse, Alonso, 2013. "Consumption and portfolio rules whit stochastic hyperbolic discounting," IKERLANAK http://www-fae1-eao1-ehu-, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    10. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
    11. Vladimir Cherny & Jan Obłój, 2013. "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model," Finance and Stochastics, Springer, vol. 17(4), pages 771-800, October.
    12. Guiyuan Ma & Song-Ping Zhu, 2022. "Revisiting the Merton Problem: from HARA to CARA Utility," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 651-686, February.
    13. Avinash N. Madavan & Subhonmesh Bose, 2021. "A Stochastic Primal-Dual Method for Optimization with Conditional Value at Risk Constraints," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 428-460, August.
    14. Qi, Yue & Liao, Kezhi & Liu, Tongyang & Zhang, Yu, 2022. "Originating multiple-objective portfolio selection by counter-COVID measures and analytically instigating robust optimization by mean-parameterized nondominated paths," Operations Research Perspectives, Elsevier, vol. 9(C).
    15. Batten, Jonathan & Hogan, Warren, 2002. "A perspective on credit derivatives," International Review of Financial Analysis, Elsevier, vol. 11(3), pages 251-278.
    16. Suleyman Basak & Anna Pavlova, 2005. "Monopoly Power and the Firm’s Valuation: A Dynamic Analysis of Short versus Long-Term Policies," Studies in Economic Theory, in: Alessandro Citanna & John Donaldson & Herakles Polemarchakis & Paolo Siconolfi & Stephan E. Spear (ed.), Essays in Dynamic General Equilibrium Theory, pages 1-34, Springer.
    17. Michael J. Klass & Krzysztof Nowicki, 2010. "On The Consumption/Distribution Theorem Under The Long-Run Growth Criterion Subject To A Drawdown Constraint," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 931-957.
    18. Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Teaching an old dog new tricks: Improved estimation of the parameters of SDEs by numerical solution of the Fokker-Planck equation," Stan Hurn Discussion Papers 2006-01, School of Economics and Finance, Queensland University of Technology.
    19. Garvey, John & Gallagher, Liam A., 2013. "The economics of data: Using simple model-free volatility in a high-frequency world," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 370-379.
    20. Zuo Quan Xu & Fahuai Yi, 2014. "An Optimal Consumption-Investment Model with Constraint on Consumption," Papers 1404.7698, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:2108.09985. 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.