Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

OPTIMAL CONSUMPTION, PORTFOLIO, AND LIFE INSURANCE WITH BORROWING CONSTRAINT AND RISK AVERSION CHANGE

  • Lee, Ho-Seok (Department of Mathematics Kwangwoon University)
  • Received : 2016.03.10
  • Accepted : 2016.05.09
  • Published : 2016.05.15
Download PDF
⟨ Previous Next ⟩

Abstract

This paper investigates an optimal consumption, portfolio, and life insurance strategies of a family when there is a borrowing constraint and risk aversion change at the time of death of the breadwinner. A CRRA utility is employed and by using the dynamic programming method, we obtain analytic expressions for the optimal strategies.

Keywords

References

  1. P. H. Dybvig and H. Liu, Lifetime consumption and investment: Retirement and constrained borrowing, Journal of Economic Theory 145 (2010), 885-907. https://doi.org/10.1016/j.jet.2009.08.003
  2. H. Huang and M. A. Milevsky, Portfolio choice and mortality-contingent claims: The general HARA case, Journal of Banking & Finance 32 (2008), 2444-2452. https://doi.org/10.1016/j.jbankfin.2008.05.002
  3. H. He and H.F. Pages, Labor income, borrowing constraints, and equilibrium asset prices, Economic Theory 3 (1993), 663-696. https://doi.org/10.1007/BF01210265
  4. B. G. Jang and H. Lee, Retirement with risk aversion change and borrowing constraints, Finance Research Letters (2015), http://dx.doi.org/10.1016/j.frl.2015.10.003.
  5. M. Kwak, Y. H. Shin, and U. J. Choi, Optimal portfolio, consumption and retirement decision under a preference change, Journal of Mathematical Analysis and Applications 355 (2009), 527-540. https://doi.org/10.1016/j.jmaa.2009.02.004
  6. M. Kwak, Y. H. Shin, and U. J. Choi, Optimal investment and consumption decision of a family with life insurance, Insurance: Mathematics and Economics 48 (2011), 176-188. https://doi.org/10.1016/j.insmatheco.2010.10.012
  7. R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, Review of Economics and Statistics 51 (1969), 247-257. https://doi.org/10.2307/1926560
  8. R. C. Merton, Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory 3 (1971), 373-413. https://doi.org/10.1016/0022-0531(71)90038-X
  9. S. R. Pliska and J. Ye, Optimal life insurance purchase and consumption/investment under uncertain lifetime, Journal of Banking & Finance 31 (2007), 1307-1319. https://doi.org/10.1016/j.jbankfin.2006.10.015
  10. S. F. Richard, Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model, Journal of Financial Economics 2 (1975), 187-203. https://doi.org/10.1016/0304-405X(75)90004-5
  11. L. R. Sotomayor and A. Cadenillas, Explicit solutions of consumption-investment problems in financial markets with regime switching, Mathematical Finance 19 (2009), 251-279. https://doi.org/10.1111/j.1467-9965.2009.00366.x
  12. S. P. Sethi, M. I. Taksar, and E. L. Presman, Explicit solution of a general consumption/portfolio problem with subsistence consumption and bankruptcy, Journal of Economic Dynamics and Control 16 (1992), 747-768. https://doi.org/10.1016/0165-1889(92)90056-K
  13. Y. Shen and J. Wei, Optimal investment-consumption-insurance with random parameters, Scandinavian Actuarial Journal 2016 (2016), 37-62. https://doi.org/10.1080/03461238.2014.900518
  14. T. Zariphopoulou, Consumptioninvestment models with constraints, SIAM Journal on Control and Optimization 32 (1994), 59-85. https://doi.org/10.1137/S0363012991218827