IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v265y2018i1p389-398.html
   My bibliography  Save this article

Semi-analytical solutions for dynamic portfolio choice in jump-diffusion models and the optimal bond-stock mix

Author

Listed:
  • Hong, Yi
  • Jin, Xing

Abstract

This paper studies the optimal portfolio selection problem in jump-diffusion models where an investor has a HARA utility function, and there are potentially a large number of assets and state variables. More specifically, we incorporate jumps into both stock returns and state variables, and then derive semi-analytical solutions for the optimal portfolio policy up to solving a set of ordinary differential equations to greatly facilitate economic insights and empirical applications of jump-diffusion models. To examine the effect of jump risk on investors’ behavior, we apply our results to the bond-stock mix problem and particularly revisit the bond/stock ratio puzzle in jump-diffusion models. Our results cast new light on this puzzle that unlike pure-diffusion models, it cannot be rationalized by the hedging demand assumption due to the presence of jumps in stock returns.

Suggested Citation

  • Hong, Yi & Jin, Xing, 2018. "Semi-analytical solutions for dynamic portfolio choice in jump-diffusion models and the optimal bond-stock mix," European Journal of Operational Research, Elsevier, vol. 265(1), pages 389-398.
    • Handle: RePEc:eee:ejores:v:265:y:2018:i:1:p:389-398
    DOI: 10.1016/j.ejor.2017.08.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717307221
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.08.010?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. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    2. Martin B. Haugh & Leonid Kogan & Jiang Wang, 2006. "Evaluating Portfolio Policies: A Duality Approach," Operations Research, INFORMS, vol. 54(3), pages 405-418, June.
    3. Xing Jin & Allen X. Zhang, 2012. "Decomposition of Optimal Portfolio Weight in a Jump-Diffusion Model and Its Applications," Review of Financial Studies, Society for Financial Studies, vol. 25(9), pages 2877-2919.
    4. 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.
    5. Robert J. Barro & Tao Jin, 2011. "On the Size Distribution of Macroeconomic Disasters," Econometrica, Econometric Society, vol. 79(5), pages 1567-1589, September.
    6. Björn Bick & Holger Kraft & Claus Munk, 2013. "Solving Constrained Consumption-Investment Problems by Simulation of Artificial Market Strategies," Management Science, INFORMS, vol. 59(2), pages 485-503, June.
    7. Jérôme B. Detemple & Ren Garcia & Marcel Rindisbacher, 2003. "A Monte Carlo Method for Optimal Portfolios," Journal of Finance, American Finance Association, vol. 58(1), pages 401-446, February.
    8. Isabelle Bajeux-Besnainou & James V. Jordan & Roland Portait, 2001. "An Asset Allocation Puzzle: Comment," American Economic Review, American Economic Association, vol. 91(4), pages 1170-1179, September.
    9. Jun Liu & Francis A. Longstaff & Jun Pan, 2003. "Dynamic Asset Allocation with Event Risk," Journal of Finance, American Finance Association, vol. 58(1), pages 231-259, February.
    10. Bardhan, Indrajit & Chao, Xiuli, 1996. "On martingale measures when asset returns have unpredictable jumps," Stochastic Processes and their Applications, Elsevier, vol. 63(1), pages 35-54, October.
    11. Canner, Niko & Mankiw, N Gregory & Weil, David N, 1997. "An Asset Allocation Puzzle," American Economic Review, American Economic Association, vol. 87(1), pages 181-191, March.
    12. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    13. Fama, Eugene F, 1981. "Stock Returns, Real Activity, Inflation, and Money," American Economic Review, American Economic Association, vol. 71(4), pages 545-565, September.
    14. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    15. Isabelle Bajeux-Besnainou & Roland Portait, 1998. "Dynamic Asset Allocation in a Mean-Variance Framework," Management Science, INFORMS, vol. 44(11-Part-2), pages 79-95, November.
    16. Antonios Sangvinatsos & Jessica A. Wachter, 2005. "Does the Failure of the Expectations Hypothesis Matter for Long‐Term Investors?," Journal of Finance, American Finance Association, vol. 60(1), pages 179-230, February.
    17. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    18. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    19. 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.
    20. Sanjiv Ranjan Das & Raman Uppal, 2004. "Systemic Risk and International Portfolio Choice," Journal of Finance, American Finance Association, vol. 59(6), pages 2809-2834, December.
    21. Michael J. Brennan & Yihong Xia, 2000. "Stochastic Interest Rates and the Bond-Stock Mix," Review of Finance, European Finance Association, vol. 4(2), pages 197-210.
    22. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, June.
    23. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    24. Lioui, Abraham, 2007. "The asset allocation puzzle is still a puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1185-1216, April.
    25. Lioui, Abraham & Poncet, Patrice, 2016. "Understanding dynamic mean variance asset allocation," European Journal of Operational Research, Elsevier, vol. 254(1), pages 320-337.
    26. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
    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. Černý, Aleš & Ruf, Johannes, 2020. "Simplified stochastic calculus with applications in economics and finance," LSE Research Online Documents on Economics 108156, London School of Economics and Political Science, LSE Library.
    2. Hong, Yi & Jin, Xing, 2022. "Pricing of variance swap rates and investment decisions of variance swaps: Evidence from a three-factor model," European Journal of Operational Research, Elsevier, vol. 303(2), pages 975-985.
    3. Černý, Aleš & Ruf, Johannes, 2021. "Simplified stochastic calculus with applications in Economics and Finance," European Journal of Operational Research, Elsevier, vol. 293(2), pages 547-560.
    4. Feng, Chengxiao & Tan, Jie & Jiang, Zhenyu & Chen, Shuang, 2020. "A generalized European option pricing model with risk management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

    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. Jérôme Detemple, 2014. "Portfolio Selection: A Review," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 1-21, April.
    2. Boyle, Phelim & Imai, Junichi & Tan, Ken Seng, 2008. "Computation of optimal portfolios using simulation-based dimension reduction," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 327-338, December.
    3. Castañeda, Pablo & Reus, Lorenzo, 2019. "Suboptimal investment behavior and welfare costs: A simulation based approach," Finance Research Letters, Elsevier, vol. 30(C), pages 170-180.
    4. Jin, Xing & Zhang, Kun, 2013. "Dynamic optimal portfolio choice in a jump-diffusion model with investment constraints," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1733-1746.
    5. Larsen, Linda Sandris & Munk, Claus, 2012. "The costs of suboptimal dynamic asset allocation: General results and applications to interest rate risk, stock volatility risk, and growth/value tilts," Journal of Economic Dynamics and Control, Elsevier, vol. 36(2), pages 266-293.
    6. Lioui, Abraham, 2013. "Time consistent vs. time inconsistent dynamic asset allocation: Some utility cost calculations for mean variance preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1066-1096.
    7. 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.
    8. Lioui, Abraham & Tarelli, Andrea, 2019. "Macroeconomic environment, money demand and portfolio choice," European Journal of Operational Research, Elsevier, vol. 274(1), pages 357-374.
    9. Chenxu Li & Olivier Scaillet & Yiwen Shen, 2020. "Wealth Effect on Portfolio Allocation in Incomplete Markets," Papers 2004.10096, arXiv.org, revised Aug 2021.
    10. 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.
    11. Ahmad Telfah, "undated". "" Do Financial Planners Take Financial Crashes In Their Advice: Dynamic Asset Allocation Under Thick Tails And Fast Volatility Updating," API-Working Paper Series 0604, Arab Planning Institute - Kuwait, Information Center.
    12. Lioui, Abraham, 2007. "The asset allocation puzzle is still a puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1185-1216, April.
    13. Gerrard, Russell & Kyriakou, Ioannis & Nielsen, Jens Perch & Vodička, Peter, 2023. "On optimal constrained investment strategies for long-term savers in stochastic environments and probability hedging," European Journal of Operational Research, Elsevier, vol. 307(2), pages 948-962.
    14. Lin, Wen-chang & Lu, Jin-ray, 2012. "Risky asset allocation and consumption rule in the presence of background risk and insurance markets," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 150-158.
    15. Hong, Yi & Jin, Xing, 2022. "Pricing of variance swap rates and investment decisions of variance swaps: Evidence from a three-factor model," European Journal of Operational Research, Elsevier, vol. 303(2), pages 975-985.
    16. John H. Cochrane, 2014. "A Mean-Variance Benchmark for Intertemporal Portfolio Theory," Journal of Finance, American Finance Association, vol. 69(1), pages 1-49, February.
    17. Thijs Kamma & Antoon Pelsser, 2019. "Near-Optimal Dynamic Asset Allocation in Financial Markets with Trading Constraints," Papers 1906.12317, arXiv.org, revised Oct 2019.
    18. Oliva, I. & Renò, R., 2018. "Optimal portfolio allocation with volatility and co-jump risk that Markowitz would like," Journal of Economic Dynamics and Control, Elsevier, vol. 94(C), pages 242-256.
    19. Farid Mkouar & Jean-Luc Prigent, 2014. "Long-Term Investment with Stochastic Interest and Inflation Rates Incompleteness and Compensating Variation," Working Papers 2014-301, Department of Research, Ipag Business School.
    20. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.

    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:ejores:v:265:y:2018:i:1:p:389-398. 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.elsevier.com/locate/eor .

    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.