英文标题：
《Optimal strategies of investment in a linear stochastic model of market》
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作者：
O.S. Rozanova, G.S. Kambarbaeva
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最新提交年份：
2015
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英文摘要：
We study the continuous time portfolio optimization model on the market where the mean returns of individual securities or asset categories are linearly dependent on underlying economic factors. We introduce the functional $Q_\\gamma$ featuring the expected earnings yield of portfolio minus a penalty term proportional with a coefficient $\\gamma$ to the variance when we keep the value of the factor levels fixed. The coefficient $\\gamma$ plays the role of a risk-aversion parameter. We find the optimal trading positions that can be obtained as the solution to a maximization problem for $Q_\\gamma$ at any moment of time. The single-factor case is analyzed in more details. We present a simple asset allocation example featuring an interest rate which affects a stock index and also serves as a second investment opportunity. We consider two possibilities: the interest rate for the bank account is governed by Vasicek-type and Cox-Ingersoll-Ross dynamics, respectively. Then we compare our results with the theory of Bielecki and Pliska where the authors employ the methods of the risk-sensitive control theory thereby using an infinite horizon objective featuring the long run expected growth rate, the asymptotic variance, and a risk-aversion parameter similar to $\\gamma$.
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中文摘要：
我们研究了在单个证券或资产类别的平均收益与潜在经济因素线性相关的市场上的连续时间投资组合优化模型。我们引入了功能性的$Q_\\gamma$，其特征是当我们保持因子水平的值固定时，投资组合的预期收益率减去与系数$\\gamma$成比例的惩罚项。系数$\\gamma$起着风险规避参数的作用。我们找到了在任何时刻都可以获得的最优交易头寸，作为Q_\\gamma$的最大化问题的解。对单因素情况进行了更详细的分析。我们给出了一个简单的资产配置示例，其特点是利率会影响股票指数，也可以作为第二个投资机会。我们考虑了两种可能性：银行账户的利率分别由Vasicek type和Cox Ingersoll-Ross dynamics控制。然后，我们将我们的结果与Bielecki和Pliska的理论进行比较，其中作者采用了风险敏感控制理论的方法，从而使用了具有长期预期增长率、渐近方差和类似于$\\gamma$的风险规避参数的无限期目标。
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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：Analysis of PDEs 偏微分方程分析
分类描述：Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE\'s, conservation laws, qualitative dynamics
存在唯一性，边界条件，线性和非线性算子，稳定性，孤子理论，可积偏微分方程，守恒律，定性动力学
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