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Numerical Solution of Dynamic Portfolio Optimization with Transaction Costs

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  • Yongyang Cai
  • Kenneth Judd
  • Rong Xu

Abstract

We apply numerical dynamic programming techniques to solve discrete-time multi-asset dynamic portfolio optimization problems with proportional transaction costs and shorting/borrowing constraints. Examples include problems with multiple assets, and many trading periods in a finite horizon problem. We also solve dynamic stochastic problems, with a portfolio including one risk-free asset, an option, and its underlying risky asset, under the existence of transaction costs and constraints. These examples show that it is now tractable to solve such problems.

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  • Yongyang Cai & Kenneth Judd & Rong Xu, 2020. "Numerical Solution of Dynamic Portfolio Optimization with Transaction Costs," Papers 2003.01809, arXiv.org.
    • Handle: RePEc:arx:papers:2003.01809
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    1. Yongyang Cai & Kenneth Judd & Greg Thain & Stephen Wright, 2015. "Solving Dynamic Programming Problems on a Computational Grid," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 261-284, February.
    2. Jules H. Kamin, 1975. "Optimal Portfolio Revision with a Proportional Transaction Cost," Management Science, INFORMS, vol. 21(11), pages 1263-1271, July.
    3. Phelim Boyle & Xiaodong Lin, 1997. "Optimal Portfolio Selection with Transaction Costs," North American Actuarial Journal, Taylor & Francis Journals, vol. 1(2), pages 27-39.
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    5. Yongyang Cai & Kenneth Judd, 2013. "Shape-preserving dynamic programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 407-421, June.
    6. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    7. 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.
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    11. 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.
    12. Yongyang Cai, 2019. "Computational Methods in Environmental and Resource Economics," Annual Review of Resource Economics, Annual Reviews, vol. 11(1), pages 59-82, October.
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    14. Abrams, Robert A & Karmarkar, Uday S, 1980. "Optimal Multiperiod Investment-Consumption Policies," Econometrica, Econometric Society, vol. 48(2), pages 333-353, March.
    15. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 7, pages 207-227, World Scientific Publishing Co. Pte. Ltd..
    16. Yongyang Cai & Kenneth Judd, 2015. "Dynamic programming with Hermite approximation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 245-267, June.
    17. Yongyang Cai & Kenneth L. Judd, 2010. "Stable and Efficient Computational Methods for Dynamic Programming," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 626-634, 04-05.
    18. Karel Janeček & Steven Shreve, 2004. "Asymptotic analysis for optimal investment and consumption with transaction costs," Finance and Stochastics, Springer, vol. 8(2), pages 181-206, May.
    19. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    20. David B. Brown & James E. Smith, 2011. "Dynamic Portfolio Optimization with Transaction Costs: Heuristics and Dual Bounds," Management Science, INFORMS, vol. 57(10), pages 1752-1770, October.
    21. Cai, Yongyang & Judd, Kenneth L., 2012. "Dynamic programming with shape-preserving rational spline Hermite interpolation," Economics Letters, Elsevier, vol. 117(1), pages 161-164.
    22. George M. Constantinides, 1976. "Note--Optimal Portfolio Revision with Proportional Transaction Costs: Extension to Hara Utility Functions and Exogenous Deterministic Income," Management Science, INFORMS, vol. 22(8), pages 921-923, April.
    23. Zabel, Edward, 1973. "Consumer Choice, Portfolio Decisions, and Transaction Costs," Econometrica, Econometric Society, vol. 41(2), pages 321-335, March.
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    1. Yongyang Cai & Kenneth Judd & Greg Thain & Stephen Wright, 2015. "Solving Dynamic Programming Problems on a Computational Grid," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 261-284, February.
    2. Areski Cousin & J'er^ome Lelong & Tom Picard, 2023. "Mean-variance dynamic portfolio allocation with transaction costs: a Wiener chaos expansion approach," Papers 2305.16152, arXiv.org, revised Jun 2023.
    3. Yongyang Cai & Kenneth Judd & Jevgenijs Steinbuks, 2017. "A nonlinear certainty equivalent approximation method for dynamic stochastic problems," Quantitative Economics, Econometric Society, vol. 8(1), pages 117-147, March.
    4. Alet Roux & Zhikang Xu, 2019. "Optimal investment and contingent claim valuation with exponential disutility under proportional transaction costs," Papers 1909.06260, arXiv.org, revised May 2021.
    5. repec:hal:wpaper:hal-04086378 is not listed on IDEAS
    6. Najafi, Amir Abbas & Pourahmadi, Zahra, 2016. "An efficient heuristic method for dynamic portfolio selection problem under transaction costs and uncertain conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 154-162.
    7. Rongju Zhang & Nicolas Langren'e & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2016. "Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach," Papers 1610.07694, arXiv.org, revised Jun 2019.
    8. Yongyang Cai & Kenneth Judd, 2015. "Dynamic programming with Hermite approximation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 245-267, June.
    9. Kumar Yashaswi, 2021. "Deep Reinforcement Learning for Portfolio Optimization using Latent Feature State Space (LFSS) Module," Papers 2102.06233, arXiv.org.
    10. Peter Schober & Julian Valentin & Dirk Pflüger, 2022. "Solving High-Dimensional Dynamic Portfolio Choice Models with Hierarchical B-Splines on Sparse Grids," Computational Economics, Springer;Society for Computational Economics, vol. 59(1), pages 185-224, January.
    11. Daniel Dimitrov, 2022. "Intergenerational Risk Sharing with Market Liquidity Risk," Tinbergen Institute Discussion Papers 22-028/VI, Tinbergen Institute.
    12. Sabastine Mushori & Delson Chikobvu, 2016. "A Stochastic Multi-stage Trading Cost model in optimal portfolio selection," EERI Research Paper Series EERI RP 2016/23, Economics and Econometrics Research Institute (EERI), Brussels.

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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