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本文引入了集值映射的锥方向的高阶广义邻近导数.应用这种导数,构建了约束的集值优化问题的一种高阶Mond-Weir型对偶,并建立了相应的弱对偶,强对偶和逆对偶性,获得的结果推广了文献中的相应结论. 相似文献
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在多维框架下提出了基于可接受集的两种风险度量概念,讨论了一些相应的性质,给出了这两种风险度量在满足一定条件下的表示定理.最后给出了几个实例. 相似文献
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在一类锥约束单目标优化问题的一阶对偶模型基础之上,建立了锥约束多目标优化问题的二阶和高阶对偶模型.在广义凸性假设下,给出了弱对偶定理,在Kuhn-Tucker约束品性下,得到了强对偶定理.最后,在弱对偶定理的基础上,利用Fritz-John型必要条件建立了逆对偶定理. 相似文献
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周志昂 《数学的实践与认识》2007,37(15):131-135
我们讨论了广义次似凸集值优化的对偶定理.首先,我们给出了广义次似凸集值优化的对偶问题.其次,我们给出了广义次似凸集值优化的对偶定理.最后,我们考虑了广义次似凸集值优化问题的标量化对偶,并给出了一系列对偶定理. 相似文献
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给出了弧式连通凸锥优化问题的强有效解和Benson真有效解的最优性条件,讨论了目标函数和约束函数均为广义弧式连通凸锥函数优化问题的近似有效解的最优性条件,给出了相应的近似Mond-Weir型对偶模型,给出了弱对偶和逆对偶定理. 相似文献
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In this paper, we study the close relationship between multivariate coherent and convex risk measures. Namely, starting from a multivariate convex risk measure, we propose a family of multivariate coherent risk measures induced by it. In return, the convex risk measure can be represented by its induced coherent risk measures. The representation result for the induced coherent risk measures is given in terms of the minimal penalty function of the convex risk measure. Finally, an example is also given.
相似文献12.
Hirbod Assa 《Mathematics and Financial Economics》2016,10(4):441-456
A coherent risk measure with a proper continuity condition cannot be defined on a large set of random variables. However, if one relaxes the sub-additivity condition and replaces it with co-monotone sub-additivity, the proper domain of risk measures can contain the set of all random variables. In this study, by replacing the sub-additivity axiom of law invariant coherent risk measures with co-monotone sub-additivity, we introduce the class of natural risk measures on the space of all bounded-below random variables. We characterize the class of natural risk measures by providing a dual representation of its members. 相似文献
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Due to their axiomatic foundation and their favorable computational properties convex risk measures are becoming a powerful
tool in financial risk management. In this paper we will review the fundamental structural concepts of convex risk measures
within the framework of convex analysis. Then we will exploit it for deriving strong duality relations in a generic portfolio
optimization context. In particular, the duality relationship can be used for designing new, efficient approximation algorithms
based on Nesterov's smoothing techniques for non-smooth convex optimization. Furthermore, the presented concepts enable us
to formalize the notion of flexibility as the (marginal) risk absorption capacity of a technology or (available) resources.
This paper is dedicated to R.T. Rockafellar for his stimulating and impressive work in convex optimization for decades. We
thank you for the insights and inspirations we gained from your fundamental research. 相似文献
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José R. Rodríguez-Mancilla 《Annals of Operations Research》2010,177(1):21-45
This paper studies some of the implicit risks associated with strategies followed by a risk averse investor who maximizes
the expected value of his final wealth, subject to a risk tolerance constraint characterized in terms of a convex risk measure
such as Conditional Value-at-Risk. Embedded probability measures are uncovered using duality theory; these are used to assess
the probability of surpassing a standard Value-at-Risk threshold. Using one of these embedded probabilities, a closed-form
measure of the financial cost of hedging the loss exposure associated to the optimal strategies is derived and shown to be,
under certain assumptions, a coherent measure of risk. 相似文献
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Riccardo Gatto Benjamin Baumgartner 《Methodology and Computing in Applied Probability》2014,16(3):561-582
We analyze the insurer risk under the compound Poisson risk process perturbed by a Wiener process with infinite time horizon. In the first part of this article, we consider the capital required to have fixed probability of ruin as a measure of risk and then a coherent extension of it, analogous to the tail value at risk. We show how both measures of risk can be efficiently computed by the saddlepoint approximation. We also show how to compute the stabilities of these measures of risk with respect to variations of probability of ruin. In the second part of this article, we are interested in the computation of the probability of ruin due to claim and the probability of ruin due to oscillation. We suggest a computational method based on upper and lower bounds of the probability of ruin and we compare it to the saddlepoint and to the Fast Fourier transform methods. This alternative method can be used to evaluate the proposed measures of risk and their stabilities with heavy-tailed individual losses, where the saddlepoint approximation cannot be used. The numerical accuracy of all proposed methods is very high and therefore these measures of risk can be reliably used in actuarial risk analysis. 相似文献
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Jiongmin Yong 《Applicable analysis》2013,92(11):1429-1442
Continuous-time dynamic convex and coherent risk measures are introduced. To obtain existence of such risk measures, backward stochastic Volterra integral equations (BSVIEs, for short) are studied. For such equations, notion of adapted M-solution is introduced, well-posedness is established, duality principles and comparison theorems are presented. Then a class of dynamic convex and coherent risk measures are identified as a component of the adapted M-solutions to certain BSVIEs. 相似文献
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We propose a novel approach to quantification of risk preferences on the space of nondecreasing functions. When applied to law invariant risk preferences among random variables, it compares their quantile functions. The axioms on quantile functions impose relations among comonotonic random variables. We infer the existence of a numerical representation of the preference relation in the form of a quantile-based measure of risk. Using conjugate duality theory by pairing the Banach space of bounded functions with the space of finitely additive measures on a suitable algebra \(\varSigma \) , we develop a variational representation of the quantile-based measures of risk. Furthermore, we introduce a notion of risk aversion based on quantile functions, which enables us to derive an analogue of Kusuoka representation of coherent law-invariant measures of risk. 相似文献
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Estimating the probabilities by which different events might occur is usually a delicate task, subject to many sources of inaccuracies. Moreover, these probabilities can change over time, leading to a very difficult evaluation of the risk induced by any particular decision. Given a set of probability measures and a set of nominal risk measures, we define in this paper the concept of robust risk measure as the worst possible of our risks when each of our probability measures is likely to occur. We study how some properties of this new object can be related with those of our nominal risk measures, such as convexity or coherence. We introduce a robust version of the Conditional Value-at-Risk (CVaR) and of entropy-based risk measures. We show how to compute and optimize the Robust CVaR using convex duality methods and illustrate its behavior using data from the New York Stock Exchange and from the NASDAQ between 2005 and 2010. 相似文献
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Based on the complete-lattice approach, a new Lagrangian type duality theory for set-valued optimization problems is presented. In contrast to previous approaches, set-valued versions for the known scalar formulas involving infimum and supremum are obtained. In particular, a strong duality theorem, which includes the existence of the dual solution, is given under very weak assumptions: The ordering cone may have an empty interior or may not be pointed. “Saddle sets” replace the usual notion of saddle points for the Lagrangian, and this concept is proven to be sufficient to show the equivalence between the existence of primal/dual solutions and strong duality on the one hand, and the existence of a saddle set for the Lagrangian on the other hand. Applications to set-valued risk measures are indicated. 相似文献
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In this paper, we extend the concept of tail subadditivity (Belles-Sampera et al., 2014a; Belles-Sampera et al., 2014b) for distortion risk measures and give sufficient and necessary conditions for a distortion risk measure to be tail subadditive. We also introduce the generalized GlueVaR risk measures, which can be used to approach any coherent distortion risk measure. To further illustrate the applications of the tail subadditivity, we propose multivariate tail distortion (MTD) risk measures and generalize the multivariate tail conditional expectation (MTCE) risk measure introduced by Landsman et al. (2016). The properties of multivariate tail distortion risk measures, such as positive homogeneity, translation invariance, monotonicity, and subadditivity, are discussed as well. Moreover, we discuss the applications of the multivariate tail distortion risk measures in capital allocations for a portfolio of risks and explore the impacts of the dependence between risks in a portfolio and extreme tail events of a risk portfolio in capital allocations. 相似文献