Stochastic Analysis on Optimal Portfolio Selection for DC Pension Plan with Stochastic Interest and Inflation Rate
- 1 Department of Mathematics, Faculty of Science, University of Botswana, Gaborone, Botswana
- 2 Department of Mathematics, Faculty of Science, University of Botswana, Gaborone, Botswana
- 3 Department of Mathematics, Faculty of Science, University of Botswana, Gaborone, Botswana
Abstract
In this paper, we study optimal investment, consumption and portfolio choice in a framework where the pension planner member (PPM) embarks on an investment policy to cover up for some certain life targets. The aim of the pension plan manager is to maximize the expectation of total wealth at the time of retirement. The investment return process comprises of risk free asset and two risky assets, and the PPM benefit lies in a complete market that is constrained by the inflation rate. Explicit solutions for constant absolute risk aversion utility functions are obtained and optimal strategies are derived by applying by dynamic programming on the Hamilton-Jacobi-Bellman (HJB) equations. Our numerical results show various effects of some economic parameters on the optimal strategies. The inflation price market risk governs the amount invested in both stock and bond, at the same time varying the premium ratio ( η ), causes effects on the investment returns. We also investigated the effects of the correlation coefficient ( ρ ) when set high on consumption rate and income rate. Finally a sensitivity analysis is graphically presented.
- Deelstra, G., Grasselli, M. and Koehl, P.F. (2003) Optimal Investment Strategies in the Presence of a Minimum Guarantee. Insurance: Mathematics and Economics, 33, 189-207. https://doi.org/10.1016/S0167-6687(03)00153-7
- Nkeki, C.I. and Nwozo, C.R. (2012) Variational Form of Classical Portfolio Strategy and Expected Wealth for a Defined Contributory. Journal of Mathematical Finance, 2, 132-139. https://doi.org/10.4236/jmf.2012.21015
- Nkeki, C.I. and Nwozo, C.R. (2013) Optimal Investment under Inflation Protection and Optimal Portfolios with Stochastic Cash Flows Strategy. International Journal of Applied Mathematics, 43, 54-63.
- Bayracktar, E. and Young, V.R. (2013) Life Insurance Purchasing to Maximize Utility of Household Consumption. North American Actuarial Journal, 17, 114-135. https://doi.org/10.1080/10920277.2013.793159
- Bruhn, K. and Steffensen, M. (2011) Household Consumption, Investment and Life Insurance. Insurance: Mathematics and Economics, 48, 315-325. https://doi.org/10.1016/j.insmatheco.2010.12.004
- Milvesky, M.A., Huang, H.X. and Wang, J. (2008) Portfolio Choice and Life Insurance: The CRRA Case. Journal of Risk and Insurance, 75, 874-872. https://doi.org/10.1111/j.1539-6975.2008.00288.x
- Milvesky, M.A., Chen, P., Ibbotson, R. and Zhu, K. (2006) Human Capital, and Life Insurance. Financial Analysts Journal, 62, 97-109.
- Mitchell, O.S., Horneff, W.J., Maurer, R.H. and Stamos, M.Z. (2009) Asset Allocation and Location over the Life Cycle with Investment-Linked Survival Contingent Payouts. Journal of Banking and Finance, 33, 1688-1699. https://doi.org/10.1016/j.jbankfin.2009.04.001
- Huang, H. and Milvesky, M.A. (2008) Portfolio Choice and Mortality-Contingent Claims: The General HARA Case. Journal of Banking and Finance, 32, 2444-2452. https://doi.org/10.1016/j.jbankfin.2008.05.002
- Yaari, M.E. (1965) Uncertain Lifetime, Life Insurance and the Theory of the Consumer. Review of Economic Studies, 32, 137-150. https://doi.org/10.2307/2296058
- Richard, S.F. (1975) Optimal Consumption, Portfolio and Life Insurance Rules for an Uncertain Lived Individual in a Continuous Time Model. Journal of Financial Economics, 2, 187-203. https://doi.org/10.1016/0304-405X(75)90004-5
- Pliska, S.F. and Ye, J. (2007) Optimal Life Insurance Purchase and Consumption/ Investment under Uncertain Lifetime. Journal of Banking and Finance, 31, 1307-1319. https://doi.org/10.1016/j.jbankfin.2006.10.015