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

Table 2

Model notations of Section 4.

For 𝑡=𝑇−1:	For 𝑡=𝑇−2,…,0:
𝜆^1𝑇−1=𝜆𝑇−1	𝜆^1𝑡=𝜆𝑡+𝜆^1𝑡+1𝑠𝑡+1
𝛽1,𝑇−1=𝜆𝑇−1𝐸(𝑄𝑇−1)−𝜖^′𝑇−1Σ𝑇−1^−1𝜑𝑇−1	𝛽1,𝑡=𝜆𝑡+𝛽1,𝑡+1𝐸(𝑄𝑡)−𝜆^1𝑡𝜖^′𝑡(Σ𝑡)^−1𝜑𝑡
𝛽2,𝑇−1=Var(𝑄𝑇−1)−𝜑^′𝑇−1Σ𝑇−1^−1𝜑𝑇−1	𝛽2,𝑡=Var(𝑄𝑡)+𝛽2,𝑡+1𝐸(𝑄^2𝑡)−𝜑^′𝑡(Σ𝑡)^−1𝜑𝑡