This paper considers an -robust optimal investment problem for a defined contribution (DC) pension plan with uncertainty about jump and diffusion risks in a mean-variance framework. Our model allows the pension manager to have different levels of ambiguity aversion, rather than only consider the extremely ambiguity-averse attitude. Moreover, in the DC pension plan, contributions are supposed to be a predetermined amount of money as premiums and the pension funds are allowed to be invested in a financial market which consists of a risk-free asset, and a risky asset satisfying a jump-diffusion process. Notice that a part of pension members could die during the accumulation phase, and their premiums should be withdrawn. Thus, we consider the return of premiums clauses by an actuarial method and assume that the surviving members will share the difference between the return and the accumulation equally. Taking account of the pension fund size and the volatility of the accumulation, a mean-variance criterion as the investment objective for the DC plan can be formulated. By applying a game theoretic framework, the equilibrium investment strategies and the corresponding equilibrium value functions can be obtained explicitly. Economic interpretations are given in the numerical simulation, which is presented to illustrate our results.
Keywords: α-Maxmin mean-variance criterion, robust DC pension investment problem, time-consistent equilibrium strategy, return of premiums clauses
@article{RO_2021__55_S1_S2983_0,
author = {Li, Danping and Bi, Junna and Hu, Mengcong},
title = {Alpha-robust mean-variance investment strategy for {DC} pension plan with uncertainty about jump-diffusion risk},
journal = {RAIRO. Operations Research},
pages = {S2983--S2997},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
doi = {10.1051/ro/2020132},
mrnumber = {4223191},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2020132/}
}
TY - JOUR AU - Li, Danping AU - Bi, Junna AU - Hu, Mengcong TI - Alpha-robust mean-variance investment strategy for DC pension plan with uncertainty about jump-diffusion risk JO - RAIRO. Operations Research PY - 2021 SP - S2983 EP - S2997 VL - 55 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2020132/ DO - 10.1051/ro/2020132 LA - en ID - RO_2021__55_S1_S2983_0 ER -
%0 Journal Article %A Li, Danping %A Bi, Junna %A Hu, Mengcong %T Alpha-robust mean-variance investment strategy for DC pension plan with uncertainty about jump-diffusion risk %J RAIRO. Operations Research %D 2021 %P S2983-S2997 %V 55 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2020132/ %R 10.1051/ro/2020132 %G en %F RO_2021__55_S1_S2983_0
Li, Danping; Bi, Junna; Hu, Mengcong. Alpha-robust mean-variance investment strategy for DC pension plan with uncertainty about jump-diffusion risk. RAIRO. Operations Research, Tome 55 (2021), pp. S2983-S2997. doi: 10.1051/ro/2020132
[1] , and , Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause. Insur. Math. Econ. 81 (2018) 78–94. | MR | DOI
[2] and , A general theory of Markovian time inconsistent stochastic control problems. Available at SSRN 1694759 (2010).
[3] , and , Mean-variance portfolio optimization with state-dependent risk aversion. Math. Financ. 24 (2014) 1–24. | MR | Zbl | DOI
[4] and , Robust portfolio choice with uncertainty about jump and diffusion risk. J. Bank. Financ. 37 (2013) 5036–5047. | DOI
[5] , and , Stochastic lifestyling: optimal dynamic asset allocation for defined-contribution pension plans. J. Econ. Dyn. Control. 30 (2006) 843–877. | MR | Zbl | DOI
[6] , , and , Asset allocation under loss aversion and minimum performance constraint in a DC pension plan with inflation risk. Insur. Math. Econ. 75 (2017) 137–150. | MR | DOI
[7] , and , Optimal design of the guarantee for defined contribution funds. J. Econ. Dyn. Control. 28 (2004) 2239–2260. | MR | Zbl | DOI
[8] , Optimal portfolio for DC pension plans under a CEV model. Insur. Math. Econ. 44 (2009) 479–490. | MR | Zbl | DOI
[9] , Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model. Insur. Math. Econ. 45 (2009) 9–18. | MR | Zbl | DOI
[10] , and , Additivity with multiple priors. J. Math. Econ. 30 (1998) 405–420. | MR | Zbl | DOI
[11] , and , Differentiating ambiguity and ambiguity attitude. J. Econ. Theor. 118 (2004) 133–173. | MR | Zbl | DOI
[12] , and , Pension funds with a minimum guarantee: a stochastic control approach. Financ. Stoch. 15 (2011) 297–342. | MR | Zbl | DOI
[13] and , Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework. Insur. Math. Econ. 57 (2014) 58–66. | MR | Zbl | DOI
[14] and , Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints. Insur. Math. Econ. 69 (2016) 224–237. | MR | DOI
[15] and , Optimal asset allocation for DC pension plans under inflation. Insur. Math. Econ. 51 (2012) 172–181. | MR | Zbl | DOI
[16] and , Optimal investment strategy for the DC plan with the return of premiums clauses in a mean-variance framework. Insur. Math. Econ. 53 (2013) 643–649. | MR | Zbl | DOI
[17] and , Optimal dynamic asset allocation strategy for ELA scheme of DC pension plan during the distribution phase. Insur. Math. Econ. 52 (2013) 404–410. | MR | Zbl | DOI
[18] , , and , Data-driven robust mean-CVaR portfolio selection under distribution ambiguity. Quant. Financ. 19 (2019) 105–121. | MR | DOI
[19] , and , A smooth model of decision making under ambiguity. Econometrica 73 (2005) 1849–1892. | MR | Zbl | DOI
[20] , and , Recursive smooth ambiguity preferences. J. Econ. Theor. 144 (2009) 930–976. | MR | Zbl | DOI
[21] and , Frailty modeling for adult and old age mortality: the application of a modified De Moivre Hazard function to sex differentials in mortality. Demograph. Res. 3 (2000) 8. | DOI
[22] , and , Alpha-robust mean-variance reinsurance-investment strategy. J. Econ. Dyn. Control. 70 (2016) 101–123. | MR | DOI
[23] , , and , Equilibrium investment strategy for DC pension plan with default risk and return of premiums clauses under CEV model. Insur. Math. Econ. 72 (2017) 6–20. | MR | DOI
[24] , Probabilistic sophistication and multiple priors. Econometrica 70 (2002) 755–764. | MR | Zbl | DOI
[25] and , Applied Stochastic Control of Jump Diffusions, 2nd edition. Springer, Berlin-Heidelberg (2007). | Zbl | MR
[26] , and , Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump-diffusion model. Insur. Math. Econ. 67 (2016) 158–172. | MR | DOI
[27] , and , Robust portfolio choice for a defined contribution pension plan with stochastic income and interest rate. Commun. Stat-Theor. M. 47 (2018) 4106–4130. | MR | DOI
[28] and , Robust optimal investment strategy for an AAM of DC pension plans with stochastic interest rate and stochastic volatility. Insur. Math. Econ. 80 (2018) 67–83. | MR | DOI
[29] and , Equilibrium investment strategy for defined-contribution pension schemes with generalized mean-variance criterion and mortality risk. Insur. Math. Econ. 64 (2015) 396–408. | MR | DOI
[30] , and , The constant elasticity of variance (CEV) model and the Legendre transform-dual solution for annuity contracts. Insur. Math. Econ. 40 (2007) 302–310. | MR | Zbl | DOI
[31] , , and , Ambiguity aversion and optimal derivative-based pension investment with stochastic income and volatility. J. Econ. Dyn. Control 88 (2018) 70–103. | MR | DOI
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