Dynamic Asset-liability Management Model Linearization

The purpose of this paper is to establish a dynamic asset and liability management model with both practicability and generality. In this framework, D-ALM model should have the ability of handling scenarios of large scale, fulfill the requirement of stability and veracity and exhibit the characteristic of risk aversion. Moreover, the model should also be easy to modify and extend to fulfill the requirement of certain investment institutions. The piecewise linearized D-ALM model proposed in this paper has settled the above problem gracefully. It can be used to approximately substitute nonlinear D-ALM models with concave utility function. The error caused by the approximation can be offset by the precision boost caused by the increase of scenario scale.The primary contribution of this paper is that this paper has established a relatively complete theoretical framework for generalized piecewise linearization method. Firstly, by substituting differential by difference, we can easily deduce the Arrow-Pratt risk aversion index of piecewise linearized object function. Secondly, in the same way, because of the inherent relationship of difference and differential, once we get the second order derivative function of a nonlinear utility function, the correspondent piecewise linearized object function can be deduced directly using the conclusion of the paper. Finally, the nonlinear objective function implied by the piecewise linear model can be easily found by calculate its limitation. Through the linkage between nonlinear model and linear model, nonlinear model can be conveniently solved.In the last part of the paper, a concrete instance of piecewise linearized D-ALM model was realized, and the detailed procedure of several critical problem was depicted. Based on this model, a large number of practices were carried out and the risk aversion characteristic and stability of D-ALM model was deeply investigated.