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A numerical approach to solve consumption-portfolio problems with predictability in income, stock prices, and house prices

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  • Farina Weiss

    (Goethe University)

Abstract

In this paper, I establish a numerical method to solve a generic consumption-portfolio choice problem with predictability in stock prices, house prices, and labor income. I generalize the SAMS method introduced by Bick et al. (Manag Sci 59:485–503, 2013) to state-dependent modifiers. I set up artificial markets to derive closed-form solutions for my life-cycle problem and transform the resulting consumption-portfolio strategies into feasible ones in the true market. To obtain transformed-feasible strategies that are close to the truly, unknown optimal strategies, I introduce state-dependent modifiers. I show that this generalization of the SAMS method reduces the welfare losses from over 10% to less than 2%.

Suggested Citation

  • Farina Weiss, 2021. "A numerical approach to solve consumption-portfolio problems with predictability in income, stock prices, and house prices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(1), pages 33-81, February.
    • Handle: RePEc:spr:mathme:v:93:y:2021:i:1:d:10.1007_s00186-020-00727-5
    DOI: 10.1007/s00186-020-00727-5
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    References listed on IDEAS

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    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," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
    2. 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.
    3. Wachter, Jessica A., 2002. "Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(1), pages 63-91, March.
    4. Kraft, Holger & Munk, Claus & Weiss, Farina, 2019. "Predictors and portfolios over the life cycle," Journal of Banking & Finance, Elsevier, vol. 100(C), pages 1-27.
    5. Holger Kraft & Claus Munk, 2011. "Optimal Housing, Consumption, and Investment Decisions over the Life Cycle," Management Science, INFORMS, vol. 57(6), pages 1025-1041, June.
    6. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    7. Cvitanic, Jaksa & Goukasian, Levon & Zapatero, Fernando, 2003. "Monte Carlo computation of optimal portfolios in complete markets," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 971-986, April.
    8. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    9. 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.
    10. 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.
    11. John H. Cochrane, 2011. "Presidential Address: Discount Rates," Journal of Finance, American Finance Association, vol. 66(4), pages 1047-1108, August.
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    More about this item

    Keywords

    Continuous-time Optimization; Hamiltion–Jacobi–Bellman equation; Optimal consumption and investment; Predictability; Intertemporal hedging;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • D14 - Microeconomics - - Household Behavior - - - Household Saving; Personal Finance

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