均值--方差准则下带约束的资产负债管理.docx

摘要
风险资产的投资组合问题首先需要解决的是两个内容:,其目的在于最小化终端财富方差所表示的投资风险,,主要考虑了两个问题:
首先,在禁止股票卖空的限制条件下讨论连续时间均值一方差投资下资产负债问题. 市场中的风险证券和负债都用扩散过程刻画,首先给出均值方差的随机控制问题,将其嵌入到一个随机二次线性控制问题中,-次随机最优控制的识别定理,应用识别定理和HJB方程求出了辅助问题和原控制问题的最优策略的显示表达式,同时获得初始资产负债管理问题的有效前沿.
其次,:通过两个黎卡提方程构造一个连续函数,并且证明这个连续函数就是HJB方程的粘性解,最后通过解黎卡提方程获得原均值一方差问题的最优投资策略和有效前沿.
关键词:均值一方差投资组合;HJB方程;粘性解;资产负债问题;有效前沿
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ABSTRACT
Risk assets portfolio problem need to solve above all is the two contents:expected return and to measure portfolio risk and return and how to balance these two means standard asset allocation need to be addressed urgently for the problem of market thesis is devoted to mean-variance portfolio selection problem in in contin..
UOUS time financial markets,where the objective is to minimize the risk of the investment which is expressed by the variance of the terminal wealth and at the same to maximize the expected terminal main problem are considered under continuous time mean—variance framework:
First of all,this paper deals with mean—variance portfolio asset—liabilitv Droblems under the constraint that short—selling of stocks is securities and debt in Market is described with diffusion ,the problem is formulated as a stochastic optimal linear—quadratic(LQ)control problem as an auxiliary problem of the initial a verification theorem for general stochastic optimal control is by applying the verification theorem and solving the HJB equation,the optimal strategies in an explicit
form for the auxiliary and initial control problem are presented,at the same time the
efficient frontier in a closed form for the initial problem is derived.
Secondly,this paper deals with asset—liability problems follow an jump-diffusion pro- ,the problem is formulate