scholarly journals A Comparison of Techniques for Dynamic Multivariate Risk Measures

2015 ◽  
pp. 3-41 ◽  
Author(s):  
Zachary Feinstein ◽  
Birgit Rudloff
Keyword(s):  
Risk Measures ◽  
Multivariate Risk ◽  
Comparison Of Techniques ◽  
Multivariate Risk Measures

CAPITAL ALLOCATION WITH MULTIVARIATE RISK MEASURES: AN AXIOMATIC APPROACH

2019 ◽  
Vol 34 (2) ◽  
pp. 297-315
Author(s):  
Linxiao Wei ◽  
Yijun Hu
Keyword(s):  
Standard Deviation ◽  
Portfolio Management ◽  
Risk Measures ◽  
Risk Measure ◽  
Axiomatic Approach ◽  
Capital Allocation ◽  
Axiom System ◽  
Multivariate Risk ◽  
Multivariate Risk Measures ◽  
Multivariate Risk Measure

AbstractCapital allocation is of central importance in portfolio management and risk-based performance measurement. Capital allocations for univariate risk measures have been extensively studied in the finance literature. In contrast to this situation, few papers dealt with capital allocations for multivariate risk measures. In this paper, we propose an axiom system for capital allocation with multivariate risk measures. We first recall the class of the positively homogeneous and subadditive multivariate risk measures, and provide the corresponding representation results. Then it is shown that for a given positively homogeneous and subadditive multivariate risk measure, there exists a capital allocation principle. Furthermore, the uniqueness of the capital allocation principe is characterized. Finally, examples are also given to derive the explicit capital allocation principles for the multivariate risk measures based on mean and standard deviation, including the multivariate mean-standard-deviation risk measures.

Properties and calculation of multivariate risk measures: MVaR and MCVaR

2013 ◽  
Vol 211 (1) ◽  
pp. 225-254 ◽  
Author(s):  
Jinwook Lee ◽  
András Prékopa
Keyword(s):  
Risk Measures ◽  
Multivariate Risk ◽  
Multivariate Risk Measures

scholarly journals MULTIVARIATE RISK MEASURES: A CONSTRUCTIVE APPROACH BASED ON SELECTIONS

2014 ◽  
Vol 26 (4) ◽  
pp. 867-900 ◽  
Author(s):  
Ilya Molchanov ◽  
Ignacio Cascos
Keyword(s):  
Risk Measures ◽  
Constructive Approach ◽  
Multivariate Risk ◽  
Multivariate Risk Measures

scholarly journals Multivariate risk measures in the non-convex setting

2019 ◽  
Vol 36 (1-4) ◽  
pp. 25-35
Author(s):  
Andreas Haier ◽  
Ilya Molchanov
Keyword(s):  
Finite Number ◽  
Transaction Costs ◽  
Risk Measures ◽  
Proportional Transaction Costs ◽  
Closed Set ◽  
Multivariate Risk ◽  
The Family ◽  
Random Closed Set ◽  
Multivariate Risk Measures ◽  
Convex Setting

Abstract The family of admissible positions in a transaction costs model is a random closed set, which is convex in case of proportional transaction costs. However, the convexity fails, e.g., in case of fixed transaction costs or when only a finite number of transfers are possible. The paper presents an approach to measure risks of such positions based on the idea of considering all selections of the portfolio and checking if one of them is acceptable. Properties and basic examples of risk measures of non-convex portfolios are presented.

scholarly journals Time consistency for scalar multivariate risk measures

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zachary Feinstein ◽  
Birgit Rudloff
Keyword(s):  
Transaction Costs ◽  
Systemic Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Time Consistency ◽  
Entire Family ◽  
Dual Representations ◽  
Multivariate Risk ◽  
Usual Scalar ◽  
Multivariate Risk Measures

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)).

scholarly journals A supermartingale relation for multivariate risk measures

2018 ◽  
Vol 18 (12) ◽  
pp. 1971-1990 ◽  
Author(s):  
Zachary Feinstein ◽  
Birgit Rudloff
Keyword(s):  
Risk Measures ◽  
Multivariate Risk ◽  
Multivariate Risk Measures
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