# Estimation of the marginal expected shortfall under asymptotic independence

@article{Cai2019EstimationOT, title={Estimation of the marginal expected shortfall under asymptotic independence}, author={Juan-Juan Cai and Eni Musta}, journal={Scandinavian Journal of Statistics}, year={2019}, volume={47}, pages={56 - 83} }

We study the asymptotic behavior of the marginal expected shortfall when the two random variables are asymptotic independent but positively associated, which is modeled by the so‐called tail dependent coefficient. We construct an estimator of the marginal expected shortfall, which is shown to be asymptotically normal. The finite sample performance of the estimator is investigated in a small simulation study. The method is also applied to estimate the expected amount of rainfall at a weather…

## 7 Citations

### Estimation of the expected shortfall given an extreme component under conditional extreme value model

- MathematicsExtremes
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For two risks, X and Y, the Marginal Expected Shortfall (MES) is defined as 𝔼[Y∣X>FX←(1−p)]$\mathbb {E}[Y\mid X>F_{X}^{\leftarrow }(1-p)]$, where FX is the distribution function of X and p is small.…

### Empirical Tail Conditional Allocation and Its Consistency under Minimal Assumptions

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Under minimal assumptions, we prove that an empirical estimator of the tail conditional allocation (TCA), also known as the marginal expected shortfall, is consistent. Examples are provided to…

### Hidden regular variation, copula models, and the limit behavior of conditional excess risk measures

- Mathematics, Computer Science
- 2018

This work elicits connections between hidden regular variation and the behavior of tail copula parameters extending previous works in this area and studies the asymptotic behavior of the aforementioned conditional excess risk measures.

### Conditional excess risk measures and multivariate regular variation

- MathematicsStatistics & Risk Modeling
- 2019

Abstract Conditional excess risk measures like Marginal Expected Shortfall and Marginal Mean Excess are designed to aid in quantifying systemic risk or risk contagion in a multivariate setting. In…

### Inference for the tail conditional allocation: large sample properties, insurance risk assessment, and compound sums of concomitants

- EconomicsSSRN Electronic Journal
- 2022

### Asymptotic results on marginal expected shortfalls for dependent risks

- MathematicsInsurance: Mathematics and Economics
- 2021

### Conditional marginal expected shortfall

- MathematicsExtremes
- 2021

In the context of bivariate random variables (Y^{(1)},Y^{(2)}), the marginal expected shortfall, defined as \mathbb E(Y^{(1)}|Y^{(2)} \ge Q_2(1-p)) for p small, where Q_2 denotes the quantile…

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