Time consistency for scalar multivariate risk measures

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2018-10-11 DOI:10.1515/strm-2019-0023

Zachary Feinstein, Birgit Rudloff

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引用次数: 11

Abstract

Abstract In this paper we present results on dynamic multivariate scalar risk measures, which arise in markets with transaction costs and systemic risk. Dual representations of such risk measures are presented. These are then used to obtain the main results of this paper on time consistency; namely, an equivalent recursive formulation of multivariate scalar risk measures to multiportfolio time consistency. We are motivated to study time consistency of multivariate scalar risk measures as the superhedging risk measure in markets with transaction costs (with a single eligible asset) (Jouini and Kallal (1995), Löhne and Rudloff (2014), Roux and Zastawniak (2016)) does not satisfy the usual scalar concept of time consistency. In fact, as demonstrated in (Feinstein and Rudloff (2021)), scalar risk measures with the same scalarization weight at all times would not be time consistent in general. The deduced recursive relation for the scalarizations of multiportfolio time consistent set-valued risk measures provided in this paper requires consideration of the entire family of scalarizations. In this way we develop a direct notion of a “moving scalarization” for scalar time consistency that corroborates recent research on scalarizations of dynamic multi-objective problems (Karnam, Ma and Zhang (2017), Kováčová and Rudloff (2021)).

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标量多变量风险度量的时间一致性

摘要在本文中，我们给出了在具有交易成本和系统风险的市场中出现的动态多变量标量风险度量的结果。提出了这种风险度量的双重表述。然后利用这些结果得到了本文关于时间一致性的主要结果；即多变量标量风险度量与多投资组合时间一致性的等价递归公式。我们有动机研究多变量标量风险度量的时间一致性，因为在具有交易成本的市场中（具有单个合格资产）的超边际风险度量（Jouini和Kallal（1995），Löhne和Rudloff（2014），Roux和Zastawniak（2016））不满足时间一致性的通常标量概念。事实上，正如（Feinstein和Rudloff（2021））所证明的那样，在任何时候具有相同标量化权重的标量风险度量通常都不是时间一致的。本文给出的多投资组合时间一致集值风险测度的标量化的递推关系需要考虑整个标量化族。通过这种方式，我们发展了标量时间一致性的“移动标量化”的直接概念，这证实了最近对动态多目标问题标量化的研究（Karnam，Ma和Zhang（2017），Kováčová和Rudloff（2021））。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.