Optimal investment of DC pension plan with two VaR constraints. (English) Zbl 07533632
Summary: In this paper, we investigate an optimal investment problem under two value-at-risk (VaR) constraints faced by a defined contribution (DC) pension fund manager. We apply a concavification technique and a Lagrange dual method to solve the problem and derive the closed-form representations of the optimal wealth and portfolio processes in terms of the state price density. Theoretical and numerical results show that the two VaR constraints can significantly impact the distribution of the optimal terminal wealth.
Keywords:
DC pension plan; utility maximization; two VaR constraints; martingale approach; Lagrange dual method; concavificationReferences:
| [1] | Basak, S., A general equilibrium model of portfolio insurance, Review of Financial Studies, 8, 4, 1059-90 (1995) · doi:10.1093/rfs/8.4.1059 |
| [2] | Björk, T., Arbitrage theory in continuous time (2009), Oxford, UK: Oxford University Press, Oxford, UK |
| [3] | Boulier, J. F.; Huang, S. J.; Taillard, G., Optimal management under stochastic interest rates: The case of a protected defined contribution pension fund, Insurance: Mathematics and Economics, 28, 2, 173-89 (2001) · Zbl 0976.91034 · doi:10.1016/S0167-6687(00)00073-1 |
| [4] | Cairns, A. J.; Blake, D.; Dowd, K., Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans, Journal of Economic Dynamics and Control, 30, 5, 843-77 (2006) · Zbl 1200.91297 · doi:10.1016/j.jedc.2005.03.009 |
| [5] | Chen, Z.; Li, Z. F.; Zeng, Y.; Sun, J. Y., Asset allocation under loss aversion and minimum performance constraint in a DC pension plan with inflation risk, Insurance: Mathematics and Economics, 75, 137-50 (2017) · Zbl 1394.91203 · doi:10.1016/j.insmatheco.2017.05.009 |
| [6] | Chen, A.; Nguyen, T.; Stadje, M., Optimal investment under var-regulation and a minimum insurance, Insurance: Mathematics and Economics, 79, 194-209 (2018) · Zbl 1401.91108 · doi:10.1016/j.insmatheco.2018.01.008 |
| [7] | Dong, Y. H.; Zheng, H., Optimal investment of DC pension plan under short-selling constraints and portfolio insurance, Insurance: Mathematics and Economics, 85, 47-59 (2019) · Zbl 1419.91357 · doi:10.1016/j.insmatheco.2018.12.005 |
| [8] | Dong, Y. H.; Zheng, H., Optimal investment with S-shaped utility and trading and value at risk constraints: An application to defined contribution pension plan, European Journal of Operational Research, 281, 2, 341-56 (2020) · Zbl 1431.91358 · doi:10.1016/j.ejor.2019.08.034 |
| [9] | Guan, G. H.; Liang, Z. X., Optimal management of DC pension plan under loss aversion and value-at-risk constraints, Insurance: Mathematics and Economics, 69, 224-37 (2016) · Zbl 1369.91197 · doi:10.1016/j.insmatheco.2016.05.014 |
| [10] | Sun, J. Y.; Li, Y. J.; Zhang, L., Robust portfolio choice for a defined contribution pension plan with stochastic income and interest rate, Communications in Statistics - Theory and Methods, 47, 17, 4106-30 (2018) · Zbl 1508.91513 · doi:10.1080/03610926.2017.1367815 |
| [11] | Vasicek, O., An equilibrium characterization of the term structure, Journal of Financial Economics, 5, 2, 177-88 (1977) · Zbl 1372.91113 · doi:10.1016/0304-405X(77)90016-2 |
| [12] | Wang, S. X.; Rong, X. M.; Zhao, H., Optimal investment and benefit payment strategy under loss aversion for target benefit pension plans, Applied Mathematics and Computation, 346, 205-18 (2019) · Zbl 1429.91296 · doi:10.1016/j.amc.2018.10.030 |
| [13] | Wu, S., Y. Dong, W. Lv, and G. Wang. 2019. Optimal asset allocation for participating contracts with mortality risk under minimum guarantee. Communications in Statistics - Theory and Methods. Advance online publication. doi:. |
| [14] | Yao, H. X.; Yang, Z.; Chen, P., Markowitz’s mean-variance defined contribution pension fund management under inflation: A continuous-time model, Insurance: Mathematics and Economics, 53, 3, 851-63 (2013) · Zbl 1290.91153 · doi:10.1016/j.insmatheco.2013.10.002 |
| [15] | Zeng, Y.; Li, D. P.; Chen, Z.; Yang, Z., Ambiguity aversion and optimal derivative-based pension investment with stochastic income and volatility, Journal of Economic Dynamics and Control, 88, 70-103 (2018) · Zbl 1401.91212 · doi:10.1016/j.jedc.2018.01.023 |
| [16] | Zhou, Q., Optimal investment for an insurer in the Lévy market: The martingale approach, Statistics & Probability Letters, 79, 14, 1602-7 (2009) · Zbl 1169.91380 · doi:10.1016/j.spl.2009.03.027 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
