Research Article

Nash Equilibrium Strategy for a DC Pension Plan with State-Dependent Risk Aversion: A Multiperiod Mean-Variance Framework

Table 1

Related parameter values under different risk aversion coefficients.

0.5[1.2621, 1.2359, 1.2096, 1.1835, 1.1573, 1.1312, 1.1051, 1.0789, 1.0527, 1.0264]
1[1.1961, 1.1758, 1.1557, 1.1357, 1.1158, 1.0962, 1.0766, 1.0573, 1.0380, 1.0190]
1.5[1.1720, 1.1540, 1.1362, 1.1186, 1.1012, 1.0839, 1.0668, 1.0499, 1.0331, 1.0165]
2[1.1595, 1.1428, 1.1263, 1.1099, 1.0937, 1.0777, 1.0618, 1.0461, 1.0306, 1.0152]

0.5[11.3765, 10.1141, 8.8793, 7.6721, 6.4924, 5.3404, 4.2162, 3.1198, 2.0515, 1.0115]
1[11.0827, 9.8759, 8.6914, 7.5290, 6.3887, 5.2701, 4.1733, 3.0980, 2.0441, 1.0115]
1.5[10.9756, 9.7897, 8.6240, 7.4783, 6.3522, 5.2457, 4.1585, 3.0906, 2.0416, 1.0115]
2[10.9203, 9.7455, 8.5895, 7.4523, 6.3336, 5.2333, 4.1511, 3.0868, 2.0404, 1.0115]

0.5[1.7505, 1.6681, 1.5875, 1.5086, 1.4314, 1.3559, 1.2819, 1.2094, 1.1383, 1.0685]
1[1.4716, 1.4190, 1.3676, 1.3175, 1.2686, 1.2210, 1.1746, 1.1293, 1.0851, 1.0420]
1.5[1.3918, 1.3480, 1.3053, 1.2637, 1.2231, 1.1835, 1.1449, 1.1073, 1.0706, 1.0349]
2[1.3548, 1.3152, 1.2766, 1.2389, 1.2021, 1.1663, 1.1313, 1.0972, 1.0640, 1.0316]

0.5[134.0229, 105.5659, 81.0721, 60.3005, 43.0159, 28.9884, 17.9931, 9.8102, 4.2240, 1.0231]
1[124.0009, 98.3661, 76.1066, 57.0511, 41.0336, 27.8925, 17.4711, 9.6169, 4.1822, 1.0231]
1.5[120.9876, 96.2109, 74.6267, 56.0869, 40.4478, 27.5699, 17.3178, 9.5603, 4.1699, 1.0231]
2[119.5493, 95.1837, 73.9225, 55.6288, 40.1698, 27.4170, 17.2453, 9.5335, 4.1641, 1.0231]

0.5[30.1796, 26.1597, 22.3770, 18.8257, 15.5001, 12.3948, 9.5046, 6.8245, 4.3499, 2.0764]
1[26.8883, 23.5215, 20.3171, 17.2705, 14.3772, 11.6329, 9.0332, 6.5740, 4.2514, 2.0613]
1.5[25.8937, 22.7275, 19.6996, 16.8061, 14.0431, 11.4068, 8.8935, 6.4997, 4.2217, 2.0563]
2[25.4191, 22.3490, 19.4057, 16.5853, 13.8844, 11.2995, 8.8272, 6.4643, 4.2075, 2.0537]

Note. For any parameter , we omit the last element of the vector, since it is determined by the boundary conditions in (11)–(15).