DOI QR코드

DOI QR Code

OPTIMAL CONSUMPTION/INVESTMENT AND LIFE INSURANCE WITH REGIME-SWITCHING FINANCIAL MARKET PARAMETERS

  • LEE, SANG IL (DEPARTMENT OF FINANCIAL ENGINEERING, AJOU UNIVERSITY) ;
  • SHIM, GYOOCHEOL (DEPARTMENT OF FINANCIAL ENGINEERING, AJOU UNIVERSITY)
  • Received : 2015.05.28
  • Accepted : 2015.07.24
  • Published : 2015.12.25

Abstract

We study optimal consumption/investment and life insurance purchase rules for a wage earner with mortality risk under regime-switching financial market conditions, in a continuous time-horizon. We apply the Markov chain approximation method and suggest an efficient algorithm using parallel computing to solve the simultaneous Hamilton-Jaccobi-Bellman equations arising from the optimization problem. We provide numerical results under the utility functions of the constant relative risk aversion type, with which we illustrate the effects of regime switching on the optimal policies by comparing them with those in the absence of regime switching.

Keywords

References

  1. M.E. Yarri Uncertain lifetime, life insurance and the theory of the consumer Review of Economic Studies, 32 (1965), 63-91.
  2. N. H. Hakansson, Optimal Investment and Consumption Strategies Under Risk, an Uncertain Lifetime, and Insurance, International Economic Review, 10(3) (1969), 443-466. https://doi.org/10.2307/2525655
  3. R.C. Merton, Lifetime portfolio selection under uncertainty: the continuous time case, The Review of Economics and Statistics 51 (1969),247-257. https://doi.org/10.2307/1926560
  4. R.C. Meron, 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
  5. S. 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
  6. S.R. Pliska and J. Ye, Optimal life insurance purchase and consumption/investment under uncertain lifetime, Journal of Banking and Finance, 31 (2007), 1307-1319. https://doi.org/10.1016/j.jbankfin.2006.10.015
  7. J. Ye, Optimal life insurance, consumption and portfolio under uncertainty: martingale methods, Proceedings of the 2007 American Control Conference, 1103-1109.
  8. J. Ye, Optimal life insurance, consumption and portfolio: A dynamic programming approach, Proceedings of the 2008 American Control Conference, 1103-1109.
  9. J. Ye, A numerical method for a continuous-time insurance-consumption-investment model, Proceedings of 2010 American Control Conference, 6897-6903.
  10. T.K. Siu,. Fair valuation of participating policies with surrender options and regime switching, Insurance: Mathematics and Economics, 37 (2005), 533-552. https://doi.org/10.1016/j.insmatheco.2005.05.007
  11. K.F.C. Yiu, J.Z. Liu and T.K. Siu andW.K. Ching, Optimal portfolios with regime switching and value-at-risk constraint, Automatica, 46(6) (2010), 979-989. https://doi.org/10.1016/j.automatica.2010.02.027
  12. C. Zhu, Optimal control of the risk process in a regime-switching environment, Automatica, 47 (2011), 1570-1579. https://doi.org/10.1016/j.automatica.2011.03.007
  13. H.J. Kushner and P. Dupuis, Numerical Methods for Stochastic control Problems in Continuous Time, 2nd ed., Springer, New York, 2001.
  14. Q.S. Song, G. Yin and Z. Zhang, Numerical methods for controlled regime-switching diffusions and regimeswitching jump diffusions, Automatica, 42 (2006), 1147-1157. https://doi.org/10.1016/j.automatica.2006.03.016
  15. G. Yin and C. Zhu, Hybrid switching diffusions: properties and applications, Springer, New York, 2010.
  16. Z. Jin and G. Yin, A numerical method for annuity-purchasing decision making to minimize the probability of financial ruin for regime-switching wealth models, International Journal of Computer Mathematics, 88(6) (2011a), 1256-1282. https://doi.org/10.1080/00207160.2010.500662
  17. Z. Jin and G. Yin, Numerical methods for dividend optimization using regime-switching jump-diffusion models, Mathematical control and related fields, 1(1) (2011b), March.
  18. Q.S. Song, G. Yin and Z. Zhang, Numerical solutions for stochastic differential games with regime switching, IEEE transactions on automatic control, 53(2) (2008), 509-521. https://doi.org/10.1109/TAC.2007.915169
  19. E.N. Zietz, An examination of the demand for life insurance, Risk Management and Insurance Review, 6(2) (2003), 159-191. https://doi.org/10.1046/J.1098-1616.2003.030.x
  20. M. Kwak, Y.H. Shin and U.J. Choi, Optimal investment and consumption decision of family with life insurance, Insurance: Mathematics and Economics, 48 (2011), 176-188. https://doi.org/10.1016/j.insmatheco.2010.10.012
  21. E. Bayraktar and V.R. Young, Life Insurance Purchasing to Maximize Utility of Household Consumption, North American Actuarial Journal, 17(2) (2013), 114-135. https://doi.org/10.1080/10920277.2013.793159
  22. H. Huang, M.A. Milevsky and J. Wang, Portfolio Choice and Life insurance: The CRRA Case, Journal of Risk and Insurance, 75(4) (2008), 847-872. https://doi.org/10.1111/j.1539-6975.2008.00288.x
  23. H. Huang and M.A. Milevsky, Portfolio choice and mortality-contingent claims: The general HARA case, Journal of Banking and Finance, 32 (2008), 2444-2452. https://doi.org/10.1016/j.jbankfin.2008.05.002
  24. G. Shim, G. 2011. Consumption/Investment Problem when the Investment Opportunity Set can be Enlarged by Information gathering, Operations Research Letters, 39(4) (2011), 283-288. https://doi.org/10.1016/j.orl.2011.04.004