空间风险测度及其局部规范:局部不变情况

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2014-01-01 DOI:10.1515/strm-2013-5001

H. Föllmer

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引用次数: 7

摘要

摘要我们考虑空间环境中的凸风险度量，其中财务状况的结果取决于网络中不同节点的状态。与统计力学中的吉布斯测度理论类似，我们讨论了给定环境下网络单节点的条件局部风险测度的全局风险测度的局部规范。在局部律不变的条件下，证明了一致的局部规范必须是熵形式的。即使在这种情况下，全局风险度量也可能不是由局部规范唯一确定的，这可以被视为“系统风险”的来源，类似于吉布斯度量理论中相变的出现

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Spatial risk measures and their local specification: The locally law-invariant case

Abstract We consider convex risk measures in a spatial setting, where the outcome of a financial position depends on the states at different nodes of a network. In analogy to the theory of Gibbs measures in Statistical Mechanics, we discuss the local specification of a global risk measure in terms of conditional local risk measures for the single nodes of the network, given their environment. Under a condition of local law invariance, we show that a consistent local specification must be of entropic form. Even in that case, a global risk measure may not be uniquely determined by the local specification, and this can be seen as a source of “systemic risk”, in analogy to the appearance of phase transitions in the theory of Gibbs measures

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来源期刊

Statistics & Risk Modeling STATISTICS & PROBABILITY-

CiteScore

1.80

自引率

6.70%

发文量

期刊介绍： Statistics & Risk Modeling (STRM) aims at covering modern methods of statistics and probabilistic modeling, and their applications to risk management in finance, insurance and related areas. The journal also welcomes articles related to nonparametric statistical methods and stochastic processes. Papers on innovative applications of statistical modeling and inference in risk management are also encouraged. Topics Statistical analysis for models in finance and insurance Credit-, market- and operational risk models Models for systemic risk Risk management Nonparametric statistical inference Statistical analysis of stochastic processes Stochastics in finance and insurance Decision making under uncertainty.