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Time consistent portfolio strategies for a general utility function

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  • Oumar Mbodji

Abstract

We study the Merton portfolio management problem within a complete market, non constant time discount rate and general utility framework. The non constant discount rate introduces time inconsistency which can be solved by introducing sub game perfect strategies. Under some asymptotic assumptions on the utility function, we show that the subgame perfect strategy is the same as the optimal strategy, provided the discount rate is replaced by the utility weighted discount rate $\rho(t,x)$ that depends on the time $t$ and wealth level $x$. A fixed point iteration is used to find $\rho$. The consumption to wealth ratio and the investment to wealth ratio are given in feedback form as functions of the value function.

Suggested Citation

  • Oumar Mbodji, 2026. "Time consistent portfolio strategies for a general utility function," Papers 2602.18157, arXiv.org.
    • Handle: RePEc:arx:papers:2602.18157
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    References listed on IDEAS

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    1. Pirvu, Traian A. & Zhang, Huayue, 2014. "Investment–consumption with regime-switching discount rates," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 142-150.
    2. repec:dau:papers:123456789/11473 is not listed on IDEAS
    3. Oumar Mbodji & Traian A. Pirvu, 2025. "Portfolio time consistency and utility weighted discount rates," Mathematics and Financial Economics, Springer, volume 19, number 2, January.
    4. Tomas Björk & Agatha Murgoci & Xun Yu Zhou, 2014. "Mean–Variance Portfolio Optimization With State-Dependent Risk Aversion," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 1-24, January.
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