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资产负债管理研究如何合理分配资产以到达最小化风险同时确保期望剩余财富(财富减去负债)达到一定水平.本文在均值-方差投资组合理论的框架下研究两类资产负债管理模型,包括带有跨期均值-方差投资目标和带有非破产约束的模型.由于在动态规划意义下,方差不具有可分性质,传统的随机最优控制方法难以直接应用.如采用处理动态均值-方差优化问题的嵌入法来解决以上问题会带来计算上的困难.本文借鉴平均场控制的思想对以上两类问题加以研究.本文假设了非常宽泛的市场模型:所有的资产都是风险资产;债务和风险资产之间存在相关性.在此市场假设模型下,本文给出了最优投资策略(控制率)的解析表达式和均值-方差有效前沿的表达形式.本研究成果为投资者提供了新的投资策略,可应用于更复杂的资产负债管理中.
Asset-liability management studies how to allocate assets reasonably to minimize risks while ensuring that the expected remaining wealth (wealth minus liabilities) reaches a certain level.This paper studies two types of asset-liability management models under the framework of mean-variance portfolio theory, Intertemporal mean-variance investment objectives and models with non-bankruptcy constraints.Due to the fact that variance is not separable in the dynamic programming sense, the traditional stochastic optimal control methods are difficult to apply directly, such as the use of dynamic mean-variance optimization Of the embedded method to solve the above problems will bring the computational difficulties.This paper refers to the idea of the average field control of these two types of problems to be studied.This paper assumes a very broad market model: all the assets are risk assets; debt and risk There is a correlation between the assets.Under this market hypothesis model, this paper gives the analytical expression of the optimal investment strategy (control rate) and the mean-variance effective frontier expression.The research results provide investors with new Investment strategy can be applied to more complex asset and liability management.