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Optimal Sharing Rule for a Household with a Portfolio Management Problem

Author

Listed:
  • Oumar Mbodji

    (Department of Mathematics and Statistics, McMaster University, Hamilton, Canada)

  • Adrien Nguyen Huu

    (CEE-M - Centre d'Economie de l'Environnement - Montpellier - FRE2010 - INRA - Institut National de la Recherche Agronomique - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

  • Traian A. A Pirvu

    (Department of Mathematics and Statistics, McMaster University, Hamilton, Canada)

Abstract

We study an intra-household decision process in the Merton financial portfolio problem.This writes as an optimal consumption-investment problem in finite horizon for the case of two separate consumption streams and a shared final wealth, in a linear social welfare setting. We show that the aggregate problem for multiple agents can be linearly separated in multiple optimal single agent problems given an optimal sharing rule of the initial endowment. Consequently, an explicit closed form solution is obtained for each subproblem, and for the household as a whole. We show the impact of asymmetric risk aversion and market price of risk on the sharing rule in a specified setting with mean-reverting price of risk, with numerical illustration.

Suggested Citation

  • Oumar Mbodji & Adrien Nguyen Huu & Traian A. A Pirvu, 2019. "Optimal Sharing Rule for a Household with a Portfolio Management Problem," Working Papers hal-00940233, HAL.
  • Handle: RePEc:hal:wpaper:hal-00940233
    Note: View the original document on HAL open archive server: https://hal.science/hal-00940233v4
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    References listed on IDEAS

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    Cited by:

    1. Raphael Soubeyran, 2019. "Incentives, Pro-social Preferences and Discrimination," Working Papers 2019.04, FAERE - French Association of Environmental and Resource Economists.

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    More about this item

    Keywords

    market price of risk; martingale techniques; martingale tech-niques JEL: G11 (primary); optimal consumption; time inconsistency; C61 (secondary); portfolio management; Portfolio optimization; household decision;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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