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Solving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function?


  • Jules Binsbergen


  • Michael Brandt



Most dynamic programming methods deployed in the portfolio choice literature involve recursions on an approximated value function. The simulation-based method proposed recently by Brandt, Goyal, Santa-Clara, and Stroud (Review of Financial Studies, 18, 831–873, 2005), relies instead on recursive uses of approximated optimal portfolio weights. We examine the relative numerical performance of these two approaches. We show that when portfolio weights are constrained by short sale restrictions for example, iterating on optimized portfolio weights leads to superior results. Value function iterations result in a lower variance but disproportionately higher bias of the solution, especially when risk aversion is high and the investment horizon is long. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Jules Binsbergen & Michael Brandt, 2007. "Solving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function?," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 355-367, May.
  • Handle: RePEc:kap:compec:v:29:y:2007:i:3:p:355-367 DOI: 10.1007/s10614-006-9073-z

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    References listed on IDEAS

    1. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
    2. Balduzzi, Pierluigi & Lynch, Anthony W., 1999. "Transaction costs and predictability: some utility cost calculations," Journal of Financial Economics, Elsevier, vol. 52(1), pages 47-78, April.
    3. Dammon, Robert M & Spatt, Chester S & Zhang, Harold H, 2001. "Optimal Consumption and Investment with Capital Gains Taxes," Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 583-616.
    4. Cochrane, John H, 1989. "The Sensitivity of Tests of the Intertemporal Allocation of Consumption to Near-Rational Alternatives," American Economic Review, American Economic Association, vol. 79(3), pages 319-337, June.
    5. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, February.
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    Cited by:

    1. Mark Broadie & Weiwei Shen, 2016. "High-Dimensional Portfolio Optimization With Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-49, June.
    2. Rongju Zhang & Nicolas Langren'e & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2017. "Sharp Target Range Strategy for Multiperiod Portfolio Choice by Decensored Least Squares Monte Carlo," Papers 1704.00416,, revised Oct 2017.
    3. Mark Broadie & Weiwei Shen, 2017. "Numerical solutions to dynamic portfolio problems with upper bounds," Computational Management Science, Springer, vol. 14(2), pages 215-227, April.
    4. 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.
    5. Legendre, François & Togola, Djibril, 2016. "Explicit solutions to dynamic portfolio choice problems: A continuous-time detour," Economic Modelling, Elsevier, vol. 58(C), pages 627-641.
    6. Xavier Warin, 2016. "The Asset Liability Management problem of a nuclear operator : a numerical stochastic optimization approach," Papers 1611.04877,
    7. repec:bla:jrinsu:v:83:y:2016:i:4:p:913-948 is not listed on IDEAS
    8. Fei Cong & Cornelis W. Oosterlee, 2017. "Accurate and Robust Numerical Methods for the Dynamic Portfolio Management Problem," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 433-458, March.
    9. 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,, revised Oct 2017.
    10. Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2015. "A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function," Annals of Operations Research, Springer, vol. 229(1), pages 121-158, June.
    11. repec:bla:stratm:v:38:y:2017:i:11:p:2168-2188 is not listed on IDEAS


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