Optimal investment, consumption and life insurance under mean-reverting returns: the complete market solution. (English) Zbl 1284.91529
Summary: This paper considers the problem of optimal investment, consumption and life insurance acquisition for a wage earner who has CRRA (constant relative risk aversion) preferences. The market model is complete, continuous, the uncertainty is driven by Brownian motion and the stock price has mean reverting drift. The problem is solved by dynamic programming approach and the HJB equation is shown to have closed form solution. Numerical experiments explore the impact market price of risk has on the optimal strategies.
References:
| [1] | Duarte, I.; Pinheiro, A.; Pinto, A.; Pliska, S., An overview of optimal life insurance purchase, consumption and investment problems, Dynamics, Games and Science, 1, 271-286 (2011) · Zbl 1246.91059 |
| [2] | Ekeland, I.; Mbodji, O.; Pirvu, T. A., Time consistent portfolio management, SIAM Journal of Financial Mathematics, 3, 57-86 (2012) · Zbl 1257.91040 |
| [3] | Horneff, W., Maurer, R., 2009, Mortality contingent claims: impact of capital market, and interest rate risk, Working Papers from University of Michigan, Michigan Retirement Research Center, http://econpapers.repec.org/paper/mrrpapers/wp222.htm; Horneff, W., Maurer, R., 2009, Mortality contingent claims: impact of capital market, and interest rate risk, Working Papers from University of Michigan, Michigan Retirement Research Center, http://econpapers.repec.org/paper/mrrpapers/wp222.htm |
| [4] | Huang, H.; Milevsky, M. A., Portfolio choice and mortality-contingent claims: the general HARA case, Journal of Banking and Finance, 32, 11, 2444-2452 (2007) |
| [5] | Kim, T. C.; Omberg, E., Dynamic nonmyopic portfolio behavior, The Review of Financial Studies, 9, 141-161 (1969) |
| [6] | Kwak, M.; Yong, H. S.; Choi, U. J., Optimal investment and consumption decision of family with life insurance, Insurance: Mathematics and Economics, 48, 176-188 (2009) · Zbl 1233.91150 |
| [7] | Merton, R. C., Lifetime portfolio selection under uncertainty: the continuous-time case, The Review of Economics and Statistics, 51, 247-257 (1969) |
| [8] | Merton, R. C., Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 3, 373-413 (1971) · Zbl 1011.91502 |
| [9] | Munk, C.; Sorensen, C., Dynamic asset allocation with stochastic income and interest rates, Journal of Financial Economics, 96, 433-462 (2010) |
| [10] | Pliska, S.; Ye, J., Optimal life insurance purchase, consumption and investment, Journal of Banking and Finance, 31, 1307-1319 (2007) |
| [11] | Richard, S., Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model, Journal of Financial Economics, 2, 187-203 (1975) |
| [12] | Watcher, J. A., Portfolio and consumption decisions under mean-reverting returns: an exact solution for complete markets, The Journal of Financial and Quantitative Analysis, 37, 63-91 (2002) |
| [13] | Yaari, M., E., Uncertain lifetime, life insurance and the theory of the consumer, Review of Economic Studies, 32, 137-150 (1965) |
| [14] | Ye, J., 2008, Optimal life insurance, consumption and portfolio: martingale methods, In: Proceedings of the 2007 American Control Conference, pp. 1103-1109.; Ye, J., 2008, Optimal life insurance, consumption and portfolio: martingale methods, In: Proceedings of the 2007 American Control Conference, pp. 1103-1109. |
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