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Optimal Portfolio, Consumption-Leisure and Retirement Choice Problem with CES Utility

초록

영어

We study optimal portfolio, consumption-leisure and retirement choice of an infinitelylived economic agent whose instantaneous preference is characterized by a constant elasticity of substitution(CES) function of consumption and leisure. We integrate in one model the optimal consumption-leisure-work choice, optimal portfolio selection, and the optimal stopping problem in which the agent chooses her retirement time. The economic agent derives utility from both consumption and leisure, and is able to adjust her supply of labor flexibly above a certain minimum work-hour, and also has a retirement option. We solve the problem analytically by considering a variational inequality arising from the dual functions of the optimal stopping problem. The optimal retirement time is characterized as the first time when her wealth exceeds a certain critical level. We provide the critical wealth level for retirement and characterize the optimal consumption-leisure and portfolio policies before and after retirement in closed forms. We also derive properties of the optimal policies. In particular, we show that consumption in general jumps around retirement.

목차

Abstract
 1. Introduction
 2. The Financial Market Model
  2.1 The Economy
  2.2 The Utility Function
 3. The Optimization Problem
 4. The Martingale Method
 5. A Solution to the Free Boundary Value Problem
 6. Liquidity Constraints
  6.1 Introduction
  6.2 The Optimization Problem
 7. Conclusion
 A. Proof of Proposition 5.1
 B. Proof of Theorem 5.3
 C. Proof of Proposition 5.2
 D. Coefficients in Proposition 6.1
 References

저자정보

  • Kyoung Jin Choi Department of Economics, University of Wisconsin-Madison, WI 53706, USA
  • Gyoocheol Shim The Bank of Korea, Seoul, 100794, Republic of Korea
  • Yong Hyun Shin Department of Mathematical Science, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 305701, Republic of Korea

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