Bull. Korean Math. Soc. 2023; 60(4): 1101-1129
Online first article July 11, 2023 Printed July 31, 2023
https://doi.org/10.4134/BKMS.b220553
Copyright © The Korean Mathematical Society.
Junkee Jeon, Hyeng Keun Koo
Kyung Hee University; Ajou University
In this study we propose a model of optimal retirement, consumption and portfolio choice of an individual agent, which encompasses a large class of the models in the literature, and provide a methodology to solve the model. Different from the traditional approach, we consider the problems before and after retirement simultaneously and identify the difference in the dual value functions as the utility value of lifetime labor. The utility value has an option nature, namely, it is the maximized value of choosing the retirement time optimally and we discover it by solving a variational inequality. Then, we discover the dual value functions by using the utility value. We discover the value function and optimal policies by establishing a duality between the value function and the dual value function. The model and approach offer a significant advantage for computation of optimal policies for a large class of problems.
Keywords: Consumption, human wealth, option value, portfolio, retirement, utility function
MSC numbers: 91G10
Supported by: This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea(NRF-2021S1A5A2A03065678).
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd