英文标题：
《Optimal Reinsurance and Investment Strategies under Mean-Variance
Criteria: Partial and Full Information》
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作者：
Shihao Zhu, Jingtao Shi
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最新提交年份：
2020
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英文摘要：
This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is formulated as a stochastic linear-quadratic (LQ) optimal control problem where the control variables are constrained. Based on the separation principle and stochastic filtering theory, the partial information problem is solved. Efficient strategies and efficient frontier are presented in closed forms via solutions to two extended stochastic Riccati equations. As a comparison, the efficient strategies and efficient frontier are given by the viscosity solution for the Hamilton-Jacobi-Bellman (HJB) equation in the full information case. Some numerical illustrations are also provided.
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中文摘要：
本文研究了均值-方差准则下保险公司的最优再保险和投资问题。风险资产价格动态方程的驱动布朗运动和收益率不能直接观测到。禁止卖空股票。该问题被描述为一个控制变量受约束的随机线性二次型（LQ）最优控制问题。基于分离原理和随机滤波理论，解决了部分信息问题。通过求解两个扩展的随机Riccati方程，以闭合形式给出了有效策略和有效前沿。作为比较，利用哈密顿-雅可比-贝尔曼（HJB）方程在全信息情况下的粘性解给出了有效策略和有效前沿。还提供了一些数字图示。
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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
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一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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