Time Consistent Strategies for Mean-Variance Asset-Liability Management Problems

Table 3

Time-consistent strategies with and without liability for 𝜆₀=𝜆₁=0.5.

𝑡	Time-consistent strategy with liability 𝑢^∗𝑡	Time-consistent strategy without liability 𝑢^∗𝑡
0	1.194𝑙0+0.903𝑥0+3.7360.107𝑙0−0.066𝑥0+0.203−0.577𝑙0+0.163𝑥0−3.939	0.903𝑥0+3.736−0.066𝑥0+0.2030.163𝑥0−3.939
1	−0.372𝑙1+1.018𝑥1+1.7430.198𝑙1−0.060𝑥1+0.095−0.633𝑙1+0.042𝑥1−1.838	1.018𝑥1+1.743−0.060𝑥1+0.0950.042𝑥1−1.838