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http://dx.doi.org/10.7858/eamj.2018.024

AN OPTIMAL CONSUMPTION AND INVESTMENT PROBLEM WITH CES UTILITY AND NEGATIVE WEALTH CONSTRAINTS  

Roh, Kum-Hwan (Department of Mathematics, Hannam University)
Publication Information
Abstract
We investigate the optimal consumption and portfolio strategies of an agent who has a constant elasticity of substitution (CES) utility function under the negative wealth constraint. We use the martingale method to derive the closed-form solution, and we give some numerical implications.
Keywords
Negative wealth constraints; CES utility; Utility maximization; Martingale methods;
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1 I. Karatzas, J.P. Lehoczky, S.P. Sethi and S.E. Shreve, Explicit Solution of a General Consumption/Investment Problem, Mathematics of Operations Research 11 (1986), no. 2, 261-294.   DOI
2 I. Karatzas, J.P. Lehoczky and S.E. Shreve, Optimal Portfolio and Consumption Decisions for a "Small Investor" on a Finite Horizon, SIAM Journal on Control and Optimization 25 (1987), no. 6, 1557-1586.   DOI
3 H.-S. Lee and Y.H. Shin, An optimal portfolio, consumption-leisure and retirement choice problem with CES utility: a dynamic programming approach, Journal of Inequalities and Applications 319 (2015), 13 pages.
4 B.H. Lim and Y.H. Shin, Optimal Investment, Consumption and Retirement Decision with Disutility and Borrowing Constraints, Quantitative Finance 11 (2011), no. 10, 1581-1592.   DOI
5 R.C. Merton, Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case, Review of Economics and Statistics 51 (1969), no. 3, 247-257.   DOI
6 R.C. Merton, Optimum Consumption and Portfolio Rules in a Continuous-Time Model, Journal of Economic Theory 3 (1971), no. 4, 373-413.   DOI
7 K. Park, M. Kang and Y.H. Shin, An Optimal Consumption, Leisure, and Investment Problem with an Option to Retire and Negative Wealth Constraints, Chaos, Solitons and Fractals 103 (2017), 374-381.   DOI
8 S. Park and B.-G. Jang, Optimal retirement strategy with a negative wealth constraint, Operations Research Letters 42 (2014), 208-212.   DOI
9 K.J. Choi, G. Shim and Y.H. Shin, Optimal Portfolio, Consumption-Leisure and Retirement Choice Problem with CES Utility, Mathematical Finance 18 (2008), no. 3, 445-472.   DOI
10 J.C. Cox and C.F. Huang, Optimum Consumption and Portfolio Policies When Asset Prices Follow a Diffusion Process, Journal of Economic Theory 49 (1989), no. 1, 33-83.   DOI
11 H. He and H. Pages, Labor Income, Borrowing Constraints, and Equilibrium Asset Prices, Economic Theory 3 (1993), no. 4, 663-696.   DOI
12 P.H. Dybvig and H. Liu, Lifetime Consumption and Investment: Retirement and Constrained Borrowing, Journal of Economic Theory 145 (2010), no. 3, 885-907.   DOI
13 E. Farhi and S. Panageas, Saving and Investing for Early Retirement: A Theoretical Analysis, Journal of Financial Economics 83 (2007), no. 1, 87-121.   DOI