英文标题：
《Constrained Quadratic Risk Minimization via Forward and Backward
Stochastic Differential Equations》
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作者：
Yusong Li and Harry Zheng
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最新提交年份：
2017
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英文摘要：
In this paper we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following the convex duality approach, we show that the necessary and sufficient optimality conditions for both the primal and dual problems can be written in terms of processes satisfying a system of FBSDEs together with other conditions. We characterise explicitly the optimal wealth and portfolio processes as functions of adjoint processes from the dual FBSDEs in a dynamic fashion and vice versa. We apply the results to solve quadratic risk minimization problems with cone-constraints and derive the explicit representations of solutions to the extended stochastic Riccati equations for such problems.
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中文摘要：
本文研究了数学金融学中的连续时间随机线性二次控制问题。我们用随机市场系数和带凸约束的投资组合策略对资产动态进行建模。根据凸对偶方法，我们证明了原问题和对偶问题的最优性的充要条件可以写成满足FBSDE系统和其他条件的过程。我们以动态方式明确地将最优财富和投资组合过程描述为对偶FBSDE伴随过程的函数，反之亦然。我们将这些结果应用于求解具有锥约束的二次风险最小化问题，并导出了这类问题的扩展随机Riccati方程解的显式表示。
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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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