An Integral Equation in Portfolio Selection with Time-Inconsistent Preferences
Mathematical Finance
2025-01-20 v2
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.
Keywords
Cite
@article{arxiv.2412.02446,
title = {An Integral Equation in Portfolio Selection with Time-Inconsistent Preferences},
author = {Zongxia Liang and Sheng Wang and Jianming Xia},
journal= {arXiv preprint arXiv:2412.02446},
year = {2025}
}