Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A MODEL OF RETIREMENT AND CONSUMPTION-PORTFOLIO CHOICE

  • Junkee Jeon (Department of Applied Mathematics Kyung Hee University) ;
  • Hyeng Keun Koo (Department of Financial Engineering Ajou University)
  • Received : 2022.08.06
  • Accepted : 2023.01.27
  • Published : 2023.07.31
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Abstract

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

Acknowledgement

This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea(NRF-2021S1A5A2A03065678).

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