IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2104.06293.html
   My bibliography  Save this paper

Analysis of optimal portfolio on finite and small time horizons for a stochastic volatility market model

Author

Listed:
  • Minglian Lin
  • Indranil SenGupta

Abstract

In this paper, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change from its current value. We consider an incomplete stochastic volatility market model, that is driven by both a Brownian motion and a jump process. At first, we obtain a closed-form formula for an approximation to the optimal portfolio in a small-time horizon. This is obtained by finding the associated Hamilton-Jacobi-Bellman integro-differential equation and then approximating the value function by constructing appropriate super-solution and sub-solution. It is shown that the true value function can be obtained by sandwiching the constructed super-solution and sub-solution. We also prove the accuracy of the approximation formulas. Finally, we provide a procedure for generating a close-to-optimal portfolio for a finite time horizon.

Suggested Citation

  • Minglian Lin & Indranil SenGupta, 2021. "Analysis of optimal portfolio on finite and small time horizons for a stochastic volatility market model," Papers 2104.06293, arXiv.org.
    • Handle: RePEc:arx:papers:2104.06293
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2104.06293
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. George Chacko & Luis M. Viceira, 2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1369-1402.
    2. Xing Jin & Allen X. Zhang, 2012. "Decomposition of Optimal Portfolio Weight in a Jump-Diffusion Model and Its Applications," The Review of Financial Studies, Society for Financial Studies, vol. 25(9), pages 2877-2919.
    3. Tao Pang, 2006. "Stochastic Portfolio Optimization With Log Utility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 869-887.
    4. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    5. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    6. Michael Roberts & Indranil SenGupta, 2020. "Sequential Hypothesis Testing in Machine Learning, and Crude Oil Price Jump Size Detection," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(5), pages 374-395, September.
    7. Rohini Kumar & Hussein Nasralah, 2016. "Asymptotic approximation of optimal portfolio for small time horizons," Papers 1611.09300, arXiv.org, revised Feb 2018.
    8. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    9. Michael Roberts & Indranil SenGupta, 2020. "Sequential hypothesis testing in machine learning, and crude oil price jump size detection," Papers 2004.08889, arXiv.org, revised Dec 2020.
    10. Milan Kumar Das & Anindya Goswami & Nimit Rana, 2016. "Risk Sensitive Portfolio Optimization in a Jump Diffusion Model with Regimes," Papers 1603.09149, arXiv.org, revised Jan 2018.
    11. T. Pang, 2004. "Portfolio Optimization Models on Infinite-Time Horizon," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 573-597, September.
    12. Michael Roberts & Indranil SenGupta, 2020. "Infinitesimal generators for two-dimensional Lévy process-driven hypothesis testing," Annals of Finance, Springer, vol. 16(1), pages 121-139, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mrudul Y. Jani & Manish R. Betheja & Amrita Bhadoriya & Urmila Chaudhari & Mohamed Abbas & Malak S. Alqahtani, 2022. "Optimal Pricing Policies with an Allowable Discount for Perishable Items under Time-Dependent Sales Price and Trade Credit," Mathematics, MDPI, vol. 10(11), pages 1-19, June.
    2. Xianfei Hui & Baiqing Sun & Indranil SenGupta & Yan Zhou & Hui Jiang, 2022. "Stochastic volatility modeling of high-frequency CSI 300 index and dynamic jump prediction driven by machine learning," Papers 2204.02891, arXiv.org, revised Jan 2023.
    3. Treena Basu & Olaf Menzer & Joshua Ward & Indranil SenGupta, 2022. "A Novel Implementation of Siamese Type Neural Networks in Predicting Rare Fluctuations in Financial Time Series," Risks, MDPI, vol. 10(2), pages 1-16, February.
    4. Minglian Lin & Indranil SenGupta, 2023. "Analysis of optimal portfolio on finite and small-time horizons for a stochastic volatility model with multiple correlated assets," Papers 2302.06778, arXiv.org, revised Dec 2023.
    5. Minglian Lin & Indranil SenGupta & William Wilson, 2023. "Estimation of VaR with jump process: application in corn and soybean markets," Papers 2311.00832, arXiv.org, revised Jun 2024.

    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. Minglian Lin & Indranil SenGupta, 2023. "Analysis of optimal portfolio on finite and small-time horizons for a stochastic volatility model with multiple correlated assets," Papers 2302.06778, arXiv.org, revised Dec 2023.
    2. Rohini Kumar & Hussein Nasralah, 2016. "Asymptotic approximation of optimal portfolio for small time horizons," Papers 1611.09300, arXiv.org, revised Feb 2018.
    3. Chenxu Li & Olivier Scaillet & Yiwen Shen, 2020. "Wealth Effect on Portfolio Allocation in Incomplete Markets," Papers 2004.10096, arXiv.org, revised Aug 2021.
    4. Yang Shen, 2020. "Effect of Variance Swap in Hedging Volatility Risk," Risks, MDPI, vol. 8(3), pages 1-34, July.
    5. Escobar, Marcos & Ferrando, Sebastian & Rubtsov, Alexey, 2015. "Robust portfolio choice with derivative trading under stochastic volatility," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 142-157.
    6. Chenxu Li & O. Scaillet & Yiwen Shen, 2020. "Decomposition of Optimal Dynamic Portfolio Choice with Wealth-Dependent Utilities in Incomplete Markets," Swiss Finance Institute Research Paper Series 20-22, Swiss Finance Institute.
    7. Francesco, MENONCIN, 2003. "Optimal Real Consumption and Asset Allocation for a HARA Investor with Labour Income," LIDAM Discussion Papers IRES 2003015, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    8. Branger, Nicole & Muck, Matthias & Seifried, Frank Thomas & Weisheit, Stefan, 2017. "Optimal portfolios when variances and covariances can jump," Journal of Economic Dynamics and Control, Elsevier, vol. 85(C), pages 59-89.
    9. Robert Cox Merton & Francisco Venegas-Martínez, 2021. "Financial Science Trends and Perspectives: A Review Article," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(1), pages 1-15, Enero - M.
    10. Francesco Menoncin & Olivier Scaillet, 2003. "Mortality Risk and Real Optimal Asset Allocation for Pension Funds," FAME Research Paper Series rp101, International Center for Financial Asset Management and Engineering.
    11. Tao Pang & Katherine Varga, 2019. "Portfolio Optimization for Assets with Stochastic Yields and Stochastic Volatility," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 691-729, August.
    12. Francesco, MENONCIN, 2002. "Investment Strategies for HARA Utility Function : A General Algebraic Approximated Solution," LIDAM Discussion Papers IRES 2002034, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    13. Robert Cox Merton & Francisco Venegas-Martínez, 2021. "Tendencias y perspectivas de la ciencia financiera: Un artículo de revisión," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(1), pages 1-15, Enero - M.
    14. Menoncin, Francesco, 2008. "The role of longevity bonds in optimal portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 343-358, February.
    15. John Y. Campbell & Luis M. Viceira & Joshua S. White, 2003. "Foreign Currency for Long-Term Investors," Economic Journal, Royal Economic Society, vol. 113(486), pages 1-25, March.
    16. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org, revised May 2015.
    17. Qian Lin & Frank Riedel, 2021. "Optimal consumption and portfolio choice with ambiguous interest rates and volatility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1189-1202, April.
    18. John Y. Campbell & Yeung Lewis Chanb & M. Viceira, 2013. "A multivariate model of strategic asset allocation," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II, chapter 39, pages 809-848, World Scientific Publishing Co. Pte. Ltd..
    19. Jean-Pierre Fouque & Ruimeng Hu & Ronnie Sircar, 2021. "Sub- and Super-solution Approach to Accuracy Analysis of Portfolio Optimization Asymptotics in Multiscale Stochastic Factor Market," Papers 2106.11510, arXiv.org, revised Oct 2021.
    20. Lu, Jin-Ray & Hwang, Chih-Chiang & Liu, Min-Luan & Lin, Chien-Yi, 2016. "An incentive problem of risk balancing in portfolio choices," The Quarterly Review of Economics and Finance, Elsevier, vol. 61(C), pages 192-200.

    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:2104.06293. 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.