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Decomposition of Optimal Dynamic Portfolio Choice with Wealth-Dependent Utilities in Incomplete Markets

Author

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  • Chenxu Li

    (Peking University - Guanghua School of Management)

  • O. Scaillet

    (University of Geneva GSEM and GFRI; Swiss Finance Institute; University of Geneva - Research Center for Statistics)

  • Yiwen Shen

    (Columbia Business School - Decision Risk and Operations)

Abstract

This paper establishes a new decomposition of optimal dynamic portfolio choice under general incomplete-market diffusion models by disentangling the fundamental impacts on optimal policy from market incompleteness and flexible wealth-dependent utilities. We derive explicit dynamics of the components for the optimal policy, and obtain an equation system for solving the shadow price of market incompleteness, which is found to be dependent on both market state and wealth level. We identify a new important hedge component for non-myopic investors to hedge the uncertainty in shadow price due to variation in wealth level. As an application, we establish and compare the decompositions of optimal policy under general models with the prevalent HARA and CRRA utilities. Under nonrandom but possibly time-varying interest rate, we solve in closed-form the HARA policy as a combination of a bond holding scheme and a corresponding CRRA strategy. Finally, we develop a simulation method to implement the decomposition of optimal policy under the general incomplete market setting, whereas existing approaches remain elusive.

Suggested Citation

  • Chenxu Li & O. Scaillet & Yiwen Shen, 2020. "Decomposition of Optimal Dynamic Portfolio Choice with Wealth-Dependent Utilities in Incomplete Markets," Swiss Finance Institute Research Paper Series 20-22, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp2022
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    References listed on IDEAS

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    Cited by:

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    More about this item

    Keywords

    optimal portfolio choice; decomposition; incomplete market; wealth-dependent utility; closed-form;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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