Academic literature on the topic 'Multivariate risk measure'

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Journal articles on the topic "Multivariate risk measure"

1

Landsman, Zinoviy, and Tomer Shushi. "Multivariate Tail Moments for Log-Elliptical Dependence Structures as Measures of Risks." Symmetry 13, no. 4 (2021): 559. http://dx.doi.org/10.3390/sym13040559.

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The class of log-elliptical distributions is well used and studied in risk measurement and actuarial science. The reason is that risks are often skewed and positive when they describe pure risks, i.e., risks in which there is no possibility of profit. In practice, risk managers confront a system of mutually dependent risks, not only one risk. Thus, it is important to measure risks while capturing their dependence structure. In this short paper, we compute the multivariate risk measures, multivariate tail conditional expectation, and multivariate tail covariance measure for the family of log-el
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2

ARARAT, ÇAĞIN, ANDREAS H. HAMEL, and BIRGIT RUDLOFF. "SET-VALUED SHORTFALL AND DIVERGENCE RISK MEASURES." International Journal of Theoretical and Applied Finance 20, no. 05 (2017): 1750026. http://dx.doi.org/10.1142/s0219024917500261.

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Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set minimization problems. The dual relationship between these two classes of multivariate risk measures is constructed via a recent Lagrange duality for set optimization. In particular, it is shown that a shortfall risk measure can be written as an intersection over a family of divergence risk measures indexed by a scalarization parameter. Examples include set-valued ver
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3

Feinstein, Zachary, and Birgit Rudloff. "Time consistency for scalar multivariate risk measures." Statistics & Risk Modeling 38, no. 3-4 (2021): 71–90. http://dx.doi.org/10.1515/strm-2019-0023.

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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
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4

Haier, Andreas, and Ilya Molchanov. "Multivariate risk measures in the non-convex setting." Statistics & Risk Modeling 36, no. 1-4 (2019): 25–35. http://dx.doi.org/10.1515/strm-2019-0002.

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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.
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5

Fougeres, Anne-Laure, and Cecile Mercadier. "Risk Measures and Multivariate Extensions of Breiman's Theorem." Journal of Applied Probability 49, no. 2 (2012): 364–84. http://dx.doi.org/10.1239/jap/1339878792.

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The modeling of insurance risks has received an increasing amount of attention because of solvency capital requirements. The ruin probability has become a standard risk measure to assess regulatory capital. In this paper we focus on discrete-time models for the finite time horizon. Several results are available in the literature to calibrate the ruin probability by means of the sum of the tail probabilities of individual claim amounts. The aim of this work is to obtain asymptotics for such probabilities under multivariate regular variation and, more precisely, to derive them from extensions of
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6

Fougeres, Anne-Laure, and Cecile Mercadier. "Risk Measures and Multivariate Extensions of Breiman's Theorem." Journal of Applied Probability 49, no. 02 (2012): 364–84. http://dx.doi.org/10.1017/s0021900200009141.

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The modeling of insurance risks has received an increasing amount of attention because of solvency capital requirements. The ruin probability has become a standard risk measure to assess regulatory capital. In this paper we focus on discrete-time models for the finite time horizon. Several results are available in the literature to calibrate the ruin probability by means of the sum of the tail probabilities of individual claim amounts. The aim of this work is to obtain asymptotics for such probabilities under multivariate regular variation and, more precisely, to derive them from extensions of
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7

Wei, Linxiao, and Yijun Hu. "CAPITAL ALLOCATION WITH MULTIVARIATE RISK MEASURES: AN AXIOMATIC APPROACH." Probability in the Engineering and Informational Sciences 34, no. 2 (2019): 297–315. http://dx.doi.org/10.1017/s0269964819000032.

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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
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8

Zuo, Baishuai, and Chuancun Yin. "Multivariate tail covariance risk measure for generalized skew-elliptical distributions." Journal of Computational and Applied Mathematics 410 (August 2022): 114210. http://dx.doi.org/10.1016/j.cam.2022.114210.

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9

Di Bernardino, E., J. M. Fernández-Ponce, F. Palacios-Rodríguez, and M. R. Rodríguez-Griñolo. "On multivariate extensions of the conditional Value-at-Risk measure." Insurance: Mathematics and Economics 61 (March 2015): 1–16. http://dx.doi.org/10.1016/j.insmatheco.2014.11.006.

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10

Hürlimann, Werner. "Multivariate Fréchet copulas and conditional value-at-risk." International Journal of Mathematics and Mathematical Sciences 2004, no. 7 (2004): 345–64. http://dx.doi.org/10.1155/s0161171204210158.

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Based on the method of copulas, we construct a parametric family of multivariate distributions using mixtures of independent conditional distributions. The new family of multivariate copulas is a convex combination of products of independent and comonotone subcopulas. It fulfills the four most desirable properties that a multivariate statistical model should satisfy. In particular, the bivariate margins belong to a simple but flexible one-parameter family of bivariate copulas, called linear Spearman copula, which is similar but not identical to the convex family of Fréchet. It is shown that th
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