Abstract
In this paper, we study an optimal portfolio, consumption-leisure and retirement choice problem for an infinitely lived economic agent with a CES utility function. Using the dynamic programming method, we obtain the value function and optimal investment, consumption, leisure, and retirement strategies in analytic form. Numerically we observe that the threshold retirement wealth level is an increasing function with respect to the elasticity of substitution.
Highlights
We consider an optimal portfolio and consumption-leisure choice problem of an infinitely lived economic agent with a voluntary retirement option and a CES utility function of consumption and leisure
The economic agent receives labor income proportional to the amount of labor supplied before retirement and enjoys full leisure after retirement at the cost of labor income
Borrowing constraints have significant effects on an economic agent’s optimal portfolio, consumption and retirement choice, and this is well documented in the literature, for example, Dybvig and Liu [ ]
Summary
We consider an optimal portfolio and consumption-leisure choice problem of an infinitely lived economic agent with a voluntary retirement option and a CES utility function of consumption and leisure. Farhi and Panageas [ ] studied the optimal portfolio, consumption and retirement choice problem of an economic agent with a Cobb-Douglas utility function and a binomial leisure rate process (l before retirement andl after retirement) using the martingale method. We observe that the threshold retirement wealth level is an increasing function with respect to the elasticity of substitution This is due to the fact that an economic agent with a large elasticity of substitution between consumption and leisure may consume more and enjoy higher utility than an economic agent with a small elasticity of substitution when the optimal leisure rate reaches the maximum leisure rate allowed while working. Section provides numerical examples with a limiting case, and Section concludes
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