摘要翻译:
本文提出了一个一般的时间不一致随机线性二次(LQ)控制问题。时间不一致是由于期望状态的二次项和目标泛函中的状态依赖项的存在而产生的。我们在开环控制类中定义了一个平衡解,而不是最优解,并通过正倒向随机微分方程流导出了平衡控制的一个充分条件。当状态为一维且问题中的系数都是确定性的时,我们找到了一个显式平衡控制。作为一个应用,我们考虑了完全金融市场中的均值-方差投资组合选择模型,其中无风险利率是时间的确定性函数,而所有其他市场参数都可能是随机过程。应用一般充分条件,得到了风险溢价既是确定性的又是随机的情况下的显式均衡策略。
---
英文标题:
《Time-Inconsistent Stochastic Linear--Quadratic Control》
---
作者:
Ying Hu, Hanqing Jin and Xun Yu Zhou
---
最新提交年份:
2011
---
分类信息:
一级分类:Mathematics 数学
二级分类:Optimization and Control 优化与控制
分类描述:Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学,线性规划,控制论,系统论,最优控制,博弈论
--
一级分类:Mathematics 数学
二级分类:Dynamical Systems 动力系统
分类描述:Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学,力学,经典的少体问题,迭代,复杂动力学,延迟微分方程
--
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
--
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
--
---
英文摘要:
In this paper, we formulate a general time-inconsistent stochastic linear--quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a 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 find an explicit equilibrium control. As an application, we then consider 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. Applying the general sufficient condition, we obtain explicit equilibrium strategies when the risk premium is both deterministic and stochastic.
---
PDF链接:
https://arxiv.org/pdf/1111.0818