DOI QR코드

DOI QR Code

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

  • Received : 2018.05.12
  • Accepted : 2018.05.27
  • Published : 2018.05.31

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

References

  1. 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. https://doi.org/10.1111/j.1467-9965.2008.00341.x
  2. 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. https://doi.org/10.1016/0022-0531(89)90067-7
  3. P.H. Dybvig and H. Liu, Lifetime Consumption and Investment: Retirement and Constrained Borrowing, Journal of Economic Theory 145 (2010), no. 3, 885-907. https://doi.org/10.1016/j.jet.2009.08.003
  4. E. Farhi and S. Panageas, Saving and Investing for Early Retirement: A Theoretical Analysis, Journal of Financial Economics 83 (2007), no. 1, 87-121. https://doi.org/10.1016/j.jfineco.2005.10.004
  5. H. He and H. Pages, Labor Income, Borrowing Constraints, and Equilibrium Asset Prices, Economic Theory 3 (1993), no. 4, 663-696. https://doi.org/10.1007/BF01210265
  6. 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. https://doi.org/10.1287/moor.11.2.261
  7. 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. https://doi.org/10.1137/0325086
  8. 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.
  9. 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. https://doi.org/10.1080/14697680903369526
  10. R.C. Merton, Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case, Review of Economics and Statistics 51 (1969), no. 3, 247-257. https://doi.org/10.2307/1926560
  11. R.C. Merton, Optimum Consumption and Portfolio Rules in a Continuous-Time Model, Journal of Economic Theory 3 (1971), no. 4, 373-413. https://doi.org/10.1016/0022-0531(71)90038-X
  12. 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. https://doi.org/10.1016/j.chaos.2017.06.017
  13. S. Park and B.-G. Jang, Optimal retirement strategy with a negative wealth constraint, Operations Research Letters 42 (2014), 208-212. https://doi.org/10.1016/j.orl.2014.02.005