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Initial Investment Choice And Optimal Future Allocations Under Time-Monotone Performance Criteria

Author

Listed:
  • M. MUSIELA

    (BNP Paribas, 10 Harewood Avenue, London NW1 6AA, UK)

  • T. ZARIPHOPOULOU

    (Oxford-Man Institute of Quantitative Finance, Eagle House, Walton Well Road, Oxford OX2 6ED, UK;
    The Mathematical Institute, University of Oxford, Oxford, UK;
    Departments of Mathematics and IROM, The University of Texas at Austin, 1 University Station, Austin, TX 78712, USA)

Abstract

The paper offers a new perspective on optimal portfolio choice by investigating how and to what extent knowledge of an investor's desirable initial investment choice can be used to determine his future optimal portfolio allocations. Optimality of investment decisions is built on the so-called forward investment performance criteria and, in particular, on the time-monotone ones. It is shown that for this class of forward criteria the desired initial allocations completely characterize the future optimal investment strategies. The analysis uses the connection between a nonlinear equation, satisfied by the local risk tolerance, and the backward heat equation. Complete solutions are provided as well as various examples.

Suggested Citation

  • M. Musiela & T. Zariphopoulou, 2011. "Initial Investment Choice And Optimal Future Allocations Under Time-Monotone Performance Criteria," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 61-81.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:01:n:s0219024911006267
    DOI: 10.1142/S0219024911006267
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    Citations

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    Cited by:

    1. Chong, Wing Fung, 2019. "Pricing and hedging equity-linked life insurance contracts beyond the classical paradigm: The principle of equivalent forward preferences," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 93-107.
    2. Mrad Mohamed, 2020. "Mixture of consistent stochastic utilities, and a priori randomness," Post-Print hal-01728554, HAL.
    3. Bahman Angoshtari, 2022. "Predictable Forward Performance Processes in Complete Markets," Papers 2206.03608, arXiv.org, revised Sep 2022.
    4. Xue Dong He & Moris S. Strub & Thaleia Zariphopoulou, 2019. "Forward Rank-Dependent Performance Criteria: Time-Consistent Investment Under Probability Distortion," Papers 1904.01745, arXiv.org.
    5. Caroline Hillairet & Sarah Kaakai & Mohamed Mrad, 2022. "Time-consistent pension policy with minimum guarantee and sustainability constraint," Papers 2207.01536, arXiv.org, revised Feb 2024.
    6. Moris S. Strub & Xun Yu Zhou, 2021. "Evolution of the Arrow–Pratt measure of risk-tolerance for predictable forward utility processes," Finance and Stochastics, Springer, vol. 25(2), pages 331-358, April.
    7. Mykhaylo Shkolnikov & Ronnie Sircar & Thaleia Zariphopoulou, 2015. "Asymptotic analysis of forward performance processes in incomplete markets and their ill-posed HJB equations," Papers 1504.03209, arXiv.org, revised Sep 2015.
    8. Bahman Angoshtari & Thaleia Zariphopoulou & Xun Yu Zhou, 2016. "Predictable Forward Performance Processes: The Binomial Case," Papers 1611.04494, arXiv.org, revised Mar 2019.
    9. Xue Dong He & Xun Yu Zhou, 2021. "Who Are I: Time Inconsistency and Intrapersonal Conflict and Reconciliation," Papers 2105.01829, arXiv.org.
    10. Tenorio Villal¢n, Angel F. & Martín Caraballo, Ana M. & Paralera Morales, Concepción & Contreras Rubio, Ignacio, 2013. "Ecuaciones diferenciales y en diferencias aplicadas a los conceptos económicos y financieros || Differential and Difference Equations Applied to Economic and Financial Concepts," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 16(1), pages 165-199, December.
    11. Xue Dong He & Moris S. Strub & Thaleia Zariphopoulou, 2021. "Forward rank‐dependent performance criteria: Time‐consistent investment under probability distortion," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 683-721, April.

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