The Book presents a survey on the principal quantitative models on Asset Liability Management in Insurance Companies and Banks. It goes through the duration and the market value approach till the stochastic optimization. The model, by using a contingent claim approach, determines the fair value of the insurance life policies. Furthermore, it shows that the value of equity can be immunized with respect to the movevement of interest rate. Moreover, the model determines the fair value of the banks liabilities accounting for the protection and the surrender possibility. Furthermore, it determines the implied duration of banks liabilities so to show that the surrender possibility will reduce the effective duration of banks liabilities. Implications for the immunization are also treated. In recent years is born the stochastic optimization by combining the asset allocation with the liabilities side by maximizing the surplus with some constraint. An analysis of interest rate models are also treated.