Optimal Variational Portfolios with Inflation Protection Strategy and Efficient Frontier of Expected Value of Wealth for a Defined Contributory Pension Scheme

Joshua O. Okoro, Charles I. Nkeki

Department of Mathematics, Faculty of Physical Sciences, University of Benin, Benin City, Nigeria.
Department of Physical Science, Faculty of Science and Engineering, Landmark University, Omu-Aran, Nigeria.

DOI: 10.4236/jmf.2013.34050                

Abstract

This paper examines optimal variational Merton portfolios (OVMP) with inflation protection strategy for a defined contribution (DC) Pension scheme. The mean and variance of the expected value of wealth for a pension plan member (PPM) are also considered in this paper. The financial market is composed of a cash account, inflation-linked bond and stock. The effective salary of the plan member is assumed to be stochastic. It was assumed that the growth rate of PPM’s salary depends on some macroeconomic factors over time. The present value of PPM’s future contribution was obtained. The sensitivity analysis of the present value of the contribution was established. The OVMP processes with inter-temporal hedging terms and inflation protection that offset any shocks to the stochastic salary of a PPM were established. The expected values of PPM’s terminal wealth, variance and efficient frontier of the three classes of assets are obtained. The efficient frontier was found to be nonlinear and parabolic in shape. In this paper, we allow the stock price to be correlated to inflation risk index, and the effective salary of the PPM is correlated to inflation and stock risks. This will enable PPMs to determine extents of the stock market returns and risks, which can influence their contributions to the scheme.

Keywords

Optimal Variational Merton Portfolios; Mean-Variance; Expected Wealth, Defined Contribution; Pension Scheme; Pension Plan Member; Inter-Temporal Hedging Terms; Stochastic Salary

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	L. Cao and Z. F. Guo, “Optimal Variance Swaps Investments,” IAENG International Journal of Applied Mathematics, Vol. 41, No. 4, 2011, 5 Pages.
[2]	L. Cao and Z. F. Guo, “Delta hedging through Deltas from a Geometric Brownian Motion Process,” Proceedings of International Conference on Applied Financial Economics, London, 30 June-2 July 2011.
[3]	P. E. Davis, “Portfolio Regulation of Life Insurance Companies and Pension Funds,” Oxford University Press, Oxford, 2000. http.//www.oecd.org/dataoecd/30/39/2401884.pdf
[4]	A. J. G. Cairns, D. Blake and K. Dowd, “Stochastic Lifestyling: Optimal Dynamic Asset Allocation for Defined Contribution Pension Plans,” Journal of Economic Dynamics & Control, Vol. 30, No. 6, 2006, pp. 843-877. http://dx.doi.org/10.1016/j.jedc.2005.03.009
[5]	S. Brawne, A. M. Milevsky and T. S. Salisbury, “Asset Allocation and the Liquidity Premium for Illiquid Annuities,” The Journal of Risk and Insurance, Vol. 70, No. 3, 2003, pp. 509-526. http://dx.doi.org/10.1111/1539-6975.t01-1-00062
[6]	G. Deelstra, M. Grasselli and P. Koehl, “Optimal design of the Guarantee for Defined Contribution Funds,” 2002. http://www.amazon.com/Optimal-design-guarantee-defined-contribution/dp/B000RQY19I
[7]	G. Deelstra, M. Grasselli and P. Koehl, “Optimal Investment Strategies in the Presence of a Minimum Guarantee,” Insurance: Mathematics and Economics, Vol. 33, No. 1, 2003, pp. 189-207. http://dx.doi.org/10.1016/S0167-6687(03)00153-7
[8]	G. Deelstra, M. Grasselli and P. Koehl, “Optimal Design of the Guarantee for Defined Contribution Funds,” Journal of Economics Dynamics and Control, Vol. 28, No. 11, 2004, pp. 2239-226. http://dx.doi.org/10.1016/j.jedc.2003.10.003
[9]	C. R. Nwozo and C. I. Nkeki, “Optimal Investment Strategy for a Defined Contributory Pension Plan in Nigeria Using Dynamic Optimization Technique,” Studies in Mathematical Sciences, Vol. 2, No. 2, 2011, pp. 43-60.
[10]	C. R. Nwozo and C. I. Nkeki, “Optimal Investment and Portfolio Strategies with Minimum Guarantee and Inflation Protection for a Defined Contribution Pension Scheme,” Studies in Mathematical Sciences, Vol. 2, No. 2, 2011, pp. 78-89.
[11]	C. R. Nwozo and C. I. Nkeki, “Optimal Portfolio and Strategic Consumption Planning in a Life-Cycle of a Pension Plan Member in A Defined Contributory Pension Scheme,” IAENG International Journal of Applied Mathematics, Vol. 41, No. 4, 2011, p. 299.
[12]	C. I. Nkeki, “On Optimal Portfolio Management of the Accumulation Phase of a Defined Contributory Pension Scheme,” Ph.D. Thesis, University of Ibadan, Ibadan, 2011.
[13]	C. I. Nkeki and C. R. Nwozo, “Variational Form of Classical Portfolio Strategy and Expected Wealth for a Defined Contributory Pension Scheme,” Journal of Mathematical Finance, Vol. 2, No. 1, 2012, 132-139. http://dx.doi.org/10.4236/jmf.2012.21015
[14]	C. I. Nkeki and C. R. Nwozo, “Optimal Investment under Inflation Protection and Optimal Portfolios with Stochastic Cash Flows Strategy,” To appear in IAENG Journal of Applied Mathematics, Vol. 43, No. 2, 2013, p. 54.