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arXiv · 2412.02446

An Integral Equation in Portfolio Selection with Time-Inconsistent Preferences

Zongxia Liang·Sheng Wang·Jianming Xia
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Abstract

This paper discusses a nonlinear integral equation arising from portfolio selection with a class of time-inconsistent preferences. We propose a unified framework requiring minimal assumptions, such as right-continuity of market coefficients and square-integrability of the market price of risk. Our main contribution is proving the existence and uniqueness of the square-integrable solution for the integral equation under mild conditions. Illustrative applications include the mean-variance portfolio selection and the utility maximization with random risk aversion.

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Zongxia Liang, Sheng Wang, Jianming Xia. 2024-12-03. An Integral Equation in Portfolio Selection with Time-Inconsistent Preferences. https://arxiv.org/abs/2412.02446

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