英文标题：
《Time-Inconsistent Stochastic Linear--Quadratic Control: Characterization
and Uniqueness of Equilibrium》
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作者：
Ying Hu (IRMAR), Hanqing Jin, Xun Yu Zhou
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最新提交年份：
2015
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英文摘要：
In this paper, we continue our study on a general time-inconsistent stochastic linear--quadratic (LQ) control problem originally formulated in [6]. We derive a necessary and sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we prove that the explicit equilibrium control constructed in \\cite{HJZ} is indeed unique. Our proof is based on the derived equivalent condition for equilibria as well as a stochastic version of the Lebesgue differentiation theorem. Finally, we show that the equilibrium strategy is unique for a mean--variance portfolio selection model in a complete financial market where the risk-free rate is a deterministic function of time but all the other market parameters are possibly stochastic processes.
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中文摘要：
在本文中，我们继续研究一个一般的时间不一致随机线性-二次（LQ）控制问题，该问题最初在[6]中提出。我们通过向前-向后的随机微分方程流导出了平衡控制的一个充要条件。当状态为一维且问题中的系数均为确定性时，我们证明了在{HJZ}中构造的显式平衡控制确实是唯一的。我们的证明基于导出的平衡点等价条件以及勒贝格微分定理的随机版本。最后，我们证明了在一个完整的金融市场中，均值-方差投资组合选择模型的均衡策略是唯一的，其中无风险利率是时间的确定函数，但所有其他市场参数可能是随机过程。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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