Application of a General Risk Management Model to Portfolio Optimization Problems with Elliptical Distributed Returns for Risk Neutral and Risk Averse Decision Makers
Application of a General Risk Management Model to Portfolio Optimization Problems with Elliptical Distributed Returns for Risk Neutral and Risk Averse Decision Makers
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一般风险管理模型在风险中性和风险厌恶决策者的椭圆分布收益投资组合优化问题中的应用
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发表时间：
2007
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通讯作者：
Hans Frenk
中科院分区：
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作者：
B. Kaynar;I. Birbil;Hans Frenk;Hans Frenk
本文研究了收益率服从多元椭圆分布的线性损失函数的投资组合问题。我们考虑两种风险度量，风险价值和条件风险价值，以及两种类型的决策者，风险中性和风险厌恶。对于风险价值，我们表明，最优解不随决策者的类型而改变。然而，这一观察结果对于条件风险价值并不正确。然后，我们表明条件风险值的目标函数可以近似蒙特卡罗模拟只使用一个单变量分布。为了求解等价的Markowitz模型，我们改进并实现了一个有限步算法。最后，进行了数值研究。
In this paper portfolio problems with linear loss functions and multivariate elliptical distributed returns are studied. We consider two risk measures, Value-at-Risk and Conditional-Value-at-Risk, and two types of decision makers, risk neutral and risk averse. For Value-at-Risk, we show that the optimal solution does not change with the type of decision maker. However, this observation is not true for Conditional-Value-at-Risk. We then show for Conditional-Value-at-Risk that the objective function can be approximated by Monte Carlo simulation using only a univariate distribution. To solve the equivalent Markowitz model, we modify and implement a finite step algorithm. Finally, a numerical study is conducted.