多期动态资产负债管理模型的研究—Mean-Field方法的应用

Study on a Multi-Period Mean-Variance Model with Liabilities—The Application of the Mean-Field Method

摘要: 本文在均值–方差准则下考虑有负债的多期有现金流追加的投资选择问题，该问题的目标函数含有盈余期望的平方这一非线性项，不能直接利用动态规划方法求解。本文通过利用mean-field方法，扩大状态空间和策略空间，使得原问题可以利用动态规划原理得出最佳策略，进而通过迭代计算，得到了有效前沿。

Abstract: This paper investigates a multi-period mean-variance portfolio selection with liabilities and sto-chastic cash flow. It is a stochastic control problem whose objective functional involves a nonlinear function of the expected earnings, so it can’t be solved by dynamic programming method directly. By enlarging the state space and the control space, we use the mean-field method to transform the initial problem to a solvable one. We get the efficient frontier by iterative calculations.