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Explicit solutions to dynamic portfolio choice problems: A continuous-time detour

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  • François Legendre

    (TEPP - Travail, Emploi et Politiques Publiques - UPEM - Université Paris-Est Marne-la-Vallée - CNRS - Centre National de la Recherche Scientifique, ERUDITE - Equipe de Recherche sur l’Utilisation des Données Individuelles en lien avec la Théorie Economique - UPEM - Université Paris-Est Marne-la-Vallée - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12)

  • Djibril Togola

    (ERUDITE - Equipe de Recherche sur l’Utilisation des Données Individuelles en lien avec la Théorie Economique - UPEM - Université Paris-Est Marne-la-Vallée - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12)

Abstract

Recently, many academic researchers have implemented different numerical procedures to solve a dynamic portfolio choice problem especially in incomplete markets. The subsequent numerical results are sometimes significantly different from one paper to another. Thus, they have all advocated the accuracy of their methods. This paper contributes to this accuracy debate by showing how to obtain some accurate numerical results without numerical approximations, for a given investment horizon. We use a dynamic programming approach in continuous-time, and illustrate the framework with one risky and one riskless asset under a power utility. The framework is flexible enough to cover all the HARA class of utility functions.

Suggested Citation

  • François Legendre & Djibril Togola, 2015. "Explicit solutions to dynamic portfolio choice problems: A continuous-time detour," Working Papers hal-01117787, HAL.
    • Handle: RePEc:hal:wpaper:hal-01117787
    DOI: 10.13140/2.1.4715.3449
    Note: View the original document on HAL open archive server: https://enpc.hal.science/hal-01117787v2
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    Cited by:

    1. Cheng, Yuyang & Escobar-Anel, Marcos, 2023. "A class of portfolio optimization solvable problems," Finance Research Letters, Elsevier, vol. 52(C).
    2. Zhu, Yichen & Escobar-Anel, Marcos, 2022. "Polynomial affine approach to HARA utility maximization with applications to OrnsteinUhlenbeck 4/2 models," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    3. Yufeng Lin & Xiaogang Wang & Yuehua Wu, 2023. "An Adaptive Multiple-Asset Portfolio Strategy with User-Specified Risk Tolerance," Mathematics, MDPI, vol. 11(7), pages 1-35, March.
    4. Cristina Sacala, 2016. "Portfolio Dynamics. A Macroeconomic Model," International Journal of Academic Research in Accounting, Finance and Management Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Accounting, Finance and Management Sciences, vol. 6(3), pages 170-176, July.

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    More about this item

    Keywords

    Dynamic portfolio choice; Long-term investing; Time aggregation; Explicit solutions; Numerical solutions JEL Classification: G11; G12;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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