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Numerical Solution of Dynamic Portfolio Optimization with Transaction Costs

  • Yongyang Cai
  • Kenneth L. Judd
  • Rong Xu

We apply numerical dynamic programming to multi-asset dynamic portfolio optimization problems with proportional transaction costs. Examples include problems with one safe asset plus two to six risky stocks, and seven to 360 trading periods in a finite horizon problem. These examples show that it is now tractable to solve such problems.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 18709.

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Date of creation: Jan 2013
Date of revision:
Handle: RePEc:nbr:nberwo:18709
Note: TWP
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  1. 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.
  2. Yongyang Cai & Kenneth L. Judd, 2012. "Dynamic Programming with Hermite Approximation," NBER Working Papers 18540, National Bureau of Economic Research, Inc.
  3. 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, 05.
  4. Gerard Gennotte & Alan Jung, 1994. "Investment Strategies under Transaction Costs: The Finite Horizon Case," Management Science, INFORMS, vol. 40(3), pages 385-404, March.
  5. Kumar Muthuraman & Haining Zha, 2008. "Simulation-Based Portfolio Optimization For Large Portfolios With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 115-134.
  6. Abrams, Robert A & Karmarkar, Uday S, 1980. "Optimal Multiperiod Investment-Consumption Policies," Econometrica, Econometric Society, vol. 48(2), pages 333-53, March.
  7. Zabel, Edward, 1973. "Consumer Choice, Portfolio Decisions, and Transaction Costs," Econometrica, Econometric Society, vol. 41(2), pages 321-35, March.
  8. Duffie, Darrell & Sun, Tong-sheng, 1990. "Transactions costs and portfolio choice in a discrete-continuous-time setting," Journal of Economic Dynamics and Control, Elsevier, vol. 14(1), pages 35-51, February.
  9. Kumar Muthuraman & Sunil Kumar, 2006. "Multidimensional Portfolio Optimization With Proportional Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 301-335.
  10. Constantinides, George M, 1986. "Capital Market Equilibrium with Transaction Costs," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 842-62, August.
  11. 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.
  12. Hong Liu, 2004. "Optimal Consumption and Investment with Transaction Costs and Multiple Risky Assets," Journal of Finance, American Finance Association, vol. 59(1), pages 289-338, 02.
  13. Jules H. Kamin, 1975. "Optimal Portfolio Revision with a Proportional Transaction Cost," Management Science, INFORMS, vol. 21(11), pages 1263-1271, July.
  14. 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.
  15. 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 247-57, August.
  16. 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.
  17. George M. Constantinides, 1979. "Multiperiod Consumption and Investment Behavior with Convex Transactions Costs," Management Science, INFORMS, vol. 25(11), pages 1127-1137, November.
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