英文标题：
《Inverse Optimization of Convex Risk Functions》
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作者：
Jonathan Yu-Meng Li
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最新提交年份：
2016
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英文摘要：
  The theory of convex risk functions has now been well established as the basis for identifying the families of risk functions that should be used in risk averse optimization problems. Despite its theoretical appeal, the implementation of a convex risk function remains difficult, as there is little guidance regarding how a convex risk function should be chosen so that it also well represents one\'s own risk preferences. In this paper, we address this issue through the lens of inverse optimization. Specifically, given solution data from some (forward) risk-averse optimization problems we develop an inverse optimization framework that generates a risk function that renders the solutions optimal for the forward problems. The framework incorporates the well-known properties of convex risk functions, namely, monotonicity, convexity, translation invariance, and law invariance, as the general information about candidate risk functions, and also the feedbacks from individuals, which include an initial estimate of the risk function and pairwise comparisons among random losses, as the more specific information. Our framework is particularly novel in that unlike classical inverse optimization, no parametric assumption is made about the risk function, i.e. it is non-parametric. We show how the resulting inverse optimization problems can be reformulated as convex programs and are polynomially solvable if the corresponding forward problems are polynomially solvable. We illustrate the imputed risk functions in a portfolio selection problem and demonstrate their practical value using real-life data.
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中文摘要：
凸风险函数理论现在已经很好地建立起来，作为识别风险规避优化问题中应使用的风险函数族的基础。尽管凸风险函数在理论上很有吸引力，但它的实现仍然很困难，因为对于如何选择凸风险函数以使其也能很好地代表自己的风险偏好，几乎没有指导。在本文中，我们通过逆优化的视角来解决这个问题。具体而言，给定一些（正向）风险规避优化问题的解数据，我们开发了一个反向优化框架，该框架生成一个风险函数，使正向问题的解达到最优。该框架结合了凸风险函数的众所周知的特性，即单调性、凸性、平移不变性和定律不变性，作为关于候选风险函数的一般信息，以及来自个人的反馈，其中包括风险函数的初始估计和随机损失之间的成对比较，作为更具体的信息。我们的框架特别新颖，因为与经典的逆优化不同，风险函数没有参数假设，即它是非参数的。我们展示了当相应的正问题是多项式可解的时，如何将得到的逆优化问题重新表示为凸规划，并且是多项式可解的。我们举例说明了投资组合选择问题中的插补风险函数，并使用实际数据证明了它们的实用价值。
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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：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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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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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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