This paper investigates the optimal control of asset allocation on a defined contribution pension plan. In our model, the plan member is allowed to invest in a risk-free asset (bank account), a risky asset (stock) and an inflation-linked bond. The dynamics of the wealth in our model take into account a certain proportion of the client’s salary paid as the contribution towards the pension fund. By applying the Hamilton-Jacobi-Bellman equation we find the explicit solutions for the CARA and CRRA utility functions. This helps us to calculate the investment strategies associated with the stock and inflation-linked bond. Finally, a numerical simulation is presented to illustrate the behaviour of the model.
Cite this paper
Keganneng, O. and Basimanebotlhe, O. (2022). Optimal Control of Assets Allocation on a Defined Contribution Pension Plan. Open Access Library Journal, 9, e7970. doi: http://dx.doi.org/10.4236/oalib.1107970.
Gao, J.W. (2008) Stochastic Optimal Control of DC Pension Funds. Insurance: Mathematics and Economics, 42, 1159-1164.
https://doi.org/10.1016/j.insmatheco.2008.03.004
Yao, H.X., Yang, Z. and Chen, P. (2013) Markowitz’s Mean-Variance Defined Contribution Pension Fund Management under Inflation: A Continuous-Time Model. Insurance: Mathematics and Economics, 53, 851-863.
https://doi.org/10.1016/j.insmatheco.2013.10.002
Haberman, S. and Vigna, E. (2002) Optimal Investment Strategies and Risk Measures in Defined Contribution Pension Schemes. Insurance: Mathematics and Economics, 31, 35-69. https://doi.org/10.1016/S0167-6687(02)00128-2
Haberman, S. and Sung, J.-H. (1994) Dynamic Approaches to Pension Funding. Insurance: Mathematics and Economics, 15, 151-162.
https://doi.org/10.1016/0167-6687(94)90791-9
Goetzmann, W.N., Ingersoll Jr., J.E. and Ross, S.A. (2003) High-Water Marks and Hedge Fund Management Contracts. The Journal of Finance, 58, 1685-1718.
https://doi.org/10.1111/1540-6261.00581
Haberman, S. (1993) Pension Funding with Time Delays and Autoregressive Rates of Investment Return. Insurance: Mathematics and Economics, 13, 45-56.
https://doi.org/10.1016/0167-6687(93)90534-V
Gaivoronski, A.A., Krylov, S. and Van der Wijst, N. (2005) Optimal Portfolio Selection and Dynamic Benchmark Tracking. European Journal of Operational Research, 163, 115-131. https://doi.org/10.1016/j.ejor.2003.12.001
Hainaut, D. and Devolder, P. (2006) A Martingale Approach Applied to the Management of Life Insurances. Institute of Actuarial Sciences, Université Catholique de Louvain, Louvain-la-Neuve, WP06, 1.
Holmstrom, B. and Milgrom, P. (1987) Aggregation and Linearity in the Provision of Intertemporal Incentives. Econometrica: Journal of the Econometric Society, 55, 303-328. https://doi.org/10.2307/1913238
Blake, D., Cairns, A.J.G. and Dowd, K. (2001) Pensionmetrics: Stochastic Pension Plan Design and Value-at-Risk during the Accumulation Phase. Insurance: Mathematics and Economics, 29, 187-215. https://doi.org/10.1016/S0167-6687(01)00082-8
Wong, B. and Lim, A. (2009) A Benchmarking Approach to Optimal Asset Allocation for Insurers and Pension Funds. Australian School of Business Research Paper, 2009ACTL07. https://doi.org/10.2139/ssrn.1448376
Vigna, E. and Haberman, S. (2001) Optimal Investment Strategy for Defined Contribution Pension Schemes. Insurance: Mathematics and Economics, 28, 233-262.
https://doi.org/10.1016/S0167-6687(00)00077-9
Xiao, J.W., Hong, Z. and Qin, C.L. (2007) The Constant Elasticity of Variance (CEV) Model and The Legendre Transform-Dual Solution for Annuity Contracts. Insurance: Mathematics and Economics, 40, Article ID: 302310.
https://doi.org/10.1016/j.insmatheco.2006.04.007
Federico, S., Gassiat, P. and Gozzi, F. (2015) Utility Maximization with Current Utility on the Wealth: Regularity of Solutions to the HJB Equation. Finance and Stochastics, 19, 415-448. https://doi.org/10.1007/s00780-015-0257-z
Emms, P. and Haberman, S. (2007) Asymptotic and Numerical Analysis of the Optimal Investment Strategy for an Insurer. Insurance: Mathematics and Economics, 40, 113-134. https://doi.org/10.1016/j.insmatheco.2006.03.003
Stabile, G. (2006) Optimal Timing of the Annuity Purchase: Combined Stochastic Control and Optimal Stopping Problem. International Journal of Theoretical and Applied Finance, 9, 151-170. https://doi.org/10.1142/S0219024906003524
Lin, C.W., Zeng, L. and Wu, H.L. (2019) Multi-Period Portfolio Optimization in a Defined Contribution Pension Plan during the Decumulation Phase. Journal of Industrial & Management Optimization, 15, 401-427.
https://doi.org/10.3934/jimo.2018059
Khorasanee, Z. (1997) Deterministic Modeling of Defined-Contribution Pension Funds. North American Actuarial Journal, 1, 83-99.
https://doi.org/10.1080/10920277.1997.10595653
Zhang, C.-B. and Hou, R.-J. (2011) Optimal Portfolios for DC Pension with Stochastic Salary. 2011 International Conference on Business Management and Electronic Information, Guangzhou, 13-15 May 2011, 589-592.
Vasicek, O. (1977) An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5, 177-188. https://doi.org/10.1016/0304-405X(77)90016-2
