Equilibrium behavioral strategy for a DC pension plan with piecewise linear state-dependent risk tolerance. (English) Zbl 07702509
Summary: We investigate the equilibrium behavioral strategy for a defined contribution (DC) pension plan during the accumulation phase in this paper. We adopt a state-dependent function to describe the risk tolerance attitude of a mean-variance (MV) investor, which is a piecewise linear function of the current wealth level with the reference point being the discounted investment target. Meanwhile, the stochastic labor income is taken into account, whose risk sources arise from both financial and non-financial markets. The extended Hamilton-Jacobi-Bellman (HJB) system of equations for our problem is presented. Explicit expressions for the suboptimal equilibrium behavioral strategy and its corresponding equilibrium value function are obtained in the suboptimal sense by the stochastic control technique. We find that the suboptimal equilibrium behavioral strategy takes a piecewise linear feedback form of the current wealth level with respect to the discounted investment target, and it also depends on the current labor income. Finally, some numerical analyses are provided to illustrate the effects of model parameters on the suboptimal equilibrium behavioral strategy and the variance-expectation curve, which shed light on our theoretical results.
MSC:
| 62-XX | Statistics |
Keywords:
DC pension plan; state-dependent risk tolerance; extended HJB equations; equilibrium behavioral strategyReferences:
| [1] | Basak, S.; Chabakauri, G., Dynamic mean-variance asset allocation, Review of Financial Studies, 23, 8, 2970-3016 (2010) · doi:10.1093/rfs/hhq028 |
| [2] | (2004) · Zbl 1068.91028 · doi:10.1016/j.insmatheco.2003.11.001 |
| [3] | Björk, T.; Khapko, M.; Murgoci, A., On time-inconsistent stochastic control in continuous time, Finance and Stochastics, 21, 2, 331-60 (2017) · Zbl 1360.49013 · doi:10.1007/s00780-017-0327-5 |
| [4] | (2014) · Zbl 1297.49038 · doi:10.1007/s00780-014-0234-y |
| [5] | Björk, T.; Murgoci, A.; Zhou, X. Y., Mean-variance portfolio optimization with state-dependent risk aversion, Mathematical Finance, 24, 1, 1-24 (2014) · Zbl 1285.91116 · doi:10.1111/j.1467-9965.2011.00515.x |
| [6] | (2004) · Zbl 1179.91230 · doi:10.1016/S0165-1889(03)00068-X |
| [7] | (2006) · Zbl 1200.91297 · doi:10.1016/j.jedc.2005.03.009 |
| [8] | Cui, X. Y.; Li, X.; Li, D.; Shi, Y., Time consistent behavioral portfolio policy for dynamic mean-variance formulation, Journal of the Operational Research Society, 68, 12, 1647-14 (2017) · doi:10.1057/s41274-017-0179-6 |
| [9] | Cui, X. Y.; Xu, L.; Zeng, Y., Continuous time mean-variance portfolio optimization with piecewise state-dependent risk aversion, Optimization Letters, 10, 8, 1681-91 (2016) · Zbl 1414.91335 · doi:10.1007/s11590-015-0970-8 |
| [10] | (2003) · Zbl 1074.91013 · doi:10.1016/S0167-6687(03)00153-7 |
| [11] | Ekeland, I., and Lazrak, A.. 2006. Being serious about non-commitment: Subgame perfect equilibrium in continuous time. Working paper. arXiv: Math/\(0604264. ####\) |
| [12] | Ekeland, I.; Pirvu, T., Investment and consumption without commitment, Mathematics and Financial Economics, 2, 1, 57-86 (2008) · Zbl 1177.91123 · doi:10.1007/s11579-008-0014-6 |
| [13] | Hu, Y.; Jin, H. Q.; Zhou, X. Y., Time-inconsistent stochastic linear-quadratic control, SIAM Journal on Control and Optimization, 50, 3, 1548-72 (2012) · Zbl 1251.93141 · doi:10.1137/110853960 |
| [14] | Kryger, E. M., and Steffensen, M.. 2010. Some solvable portfolio problems with quadratic and collective objectives. Working paper. \(####\) |
| [15] | Li, Y. W.; Li, Z. F., Optimal time-consistent investment and reinsurance strategies for mean-variance insurers with state dependent risk aversion, Insurance: Mathematics and Economics, 53, 1, 86-97 (2013) · Zbl 1284.91249 · doi:10.1016/j.insmatheco.2013.03.008 |
| [16] | (2011) · Zbl 1218.91088 · doi:10.1016/j.insmatheco.2011.02.003 |
| [17] | Markowitz, H., Portfolio Selection, The Journal of Finance, 7, 1, 77-91 (1952) |
| [18] | Strotz, R. H., Myopia and inconsistency in dynamic utility maximization, The Review of Economic Studies, 23, 3, 165-80 (1955) · doi:10.2307/2295722 |
| [19] | Wang, J.; Forsyth, P. A., Continuous time mean variance asset allocation: A time-consistent strategy, European Journal of Operational Research, 209, 2, 184-201 (2011) · Zbl 1208.91139 · doi:10.1016/j.ejor.2010.09.038 |
| [20] | Wei, J.; Wong, K. C.; Yam, S. C. P.; Yung, S. P., Markowitz’s mean-variance asset-liability management with regime switching: A time consistent approach, Insurance: Mathematics and Economics, 53, 1, 281-91 (2013) · Zbl 1284.91533 · doi:10.1016/j.insmatheco.2013.05.008 |
| [21] | Wu, H. L., Time-consistent strategies for a multiperiod mean-variance portfolio selection problem, Journal of Applied Mathematics, 2013, 4, 1-724 (2013) · Zbl 1266.91096 · doi:10.1155/2013/841627 |
| [22] | (2015) · Zbl 1318.91125 · doi:10.1016/j.insmatheco.2015.03.014 |
| [23] | Yang, P.; Chen, Z.; Wang, L., Time-consistent reinsurance and investment strategy combining quota-share and excess of loss for mean-variance insurers with jump-diffusion price process, Communications in Statistics - Theory and Methods, 50, 11, 2546-68 (2021) · Zbl 07533682 · doi:10.1080/03610926.2019.1670849 |
| [24] | Yang, P.; Chen, Z.; Xu, Y., Time-consistent equilibrium reinsurance-investment strategy for n competitive insurers under a new interaction mechanism and a general investment framework, Journal of Computational and Applied Mathematics, 374, 112769 (2020) · Zbl 1435.62375 · doi:10.1016/j.cam.2020.112769 |
| [25] | Zeng, Y.; Li, Z. F., Optimal time-consistent investment and reinsurance policies for mean-variance insurers, Insurance: Mathematics and Economics, 49, 1, 145-54 (2011) · Zbl 1218.91167 · doi:10.1016/j.insmatheco.2011.01.001 |
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.
