英文标题：
《Dynamic portfolio selection without risk-free assets》
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作者：
Chi Kin Lam, Yuhong Xu, Guosheng Yin
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最新提交年份：
2016
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英文摘要：
We consider the mean--variance portfolio optimization problem under the game theoretic framework and without risk-free assets. The problem is solved semi-explicitly by applying the extended Hamilton--Jacobi--Bellman equation. Although the coefficient of risk aversion in our model is a constant, the optimal amounts of money invested in each stock still depend on the current wealth in general. The optimal solution is obtained by solving a system of ordinary differential equations whose existence and uniqueness are proved and a numerical algorithm as well as its convergence speed are provided. Different from portfolio selection with risk-free assets, our value function is quadratic in the current wealth, and the equilibrium allocation is linearly sensitive to the initial wealth. Numerical results show that this model performs better than both the classical one and the variance model in a bull market.
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中文摘要：
我们在博弈论框架下考虑了无风险资产的均值-方差投资组合优化问题。通过应用扩展的Hamilton--Jacobi--Bellman方程，半显式地解决了这个问题。虽然我们的模型中的风险规避系数是一个常数，但投资于每只股票的最佳资金量通常仍取决于当前的财富。通过求解一组常微分方程组得到最优解，证明了该方程组的存在唯一性，给出了数值算法及其收敛速度。与无风险资产的投资组合不同，我们的价值函数是当前财富的二次函数，均衡配置对初始财富具有线性敏感性。数值结果表明，该模型在牛市中的表现优于经典模型和方差模型。
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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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