scholarly journals Tail Conditional Expectations for Exponential Dispersion Models

2005 ◽  
Vol 35 (1) ◽  
pp. 189-209 ◽  
Author(s):  
Zinoviy Landsman ◽  
Emiliano A. Valdez
Keyword(s):  
Conditional Expectation ◽  
Value At Risk ◽  
Risk Measure ◽  
Inverse Gaussian ◽  
Dispersion Models ◽  
Average Amount ◽  
Tail Conditional Expectation ◽  
Conditional Expectations ◽  
Exponential Dispersion Models ◽  
Fixed Period

There is a growing interest in the use of the tail conditional expectation as a measure of risk. For an institution faced with a random loss, the tail conditional expectation represents the conditional average amount of loss that can be incurred in a fixed period, given that the loss exceeds a specified value. This value is typically based on the quantile of the loss distribution, the so-called value-at-risk. The tail conditional expectation can therefore provide a measure of the amount of capital needed due to exposure to loss. This paper examines this risk measure for “exponential dispersion models”, a wide and popular class of distributions to actuaries which, on one hand, generalizes the Normal and shares some of its many important properties, but on the other hand, contains many distributions of nonnegative random variables like the Gamma and the Inverse Gaussian.

scholarly journals Tail Conditional Expectations for Exponential Dispersion Models

2005 ◽  
Vol 35 (01) ◽  
pp. 189-209 ◽  
Author(s):  
Zinoviy Landsman ◽  
Emiliano A. Valdez
Keyword(s):  
Conditional Expectation ◽  
Value At Risk ◽  
Risk Measure ◽  
Inverse Gaussian ◽  
Dispersion Models ◽  
Average Amount ◽  
Tail Conditional Expectation ◽  
Conditional Expectations ◽  
Exponential Dispersion Models ◽  
Fixed Period

There is a growing interest in the use of the tail conditional expectation as a measure of risk. For an institution faced with a random loss, the tail conditional expectation represents the conditional average amount of loss that can be incurred in a fixed period, given that the loss exceeds a specified value. This value is typically based on the quantile of the loss distribution, the so-called value-at-risk. The tail conditional expectation can therefore provide a measure of the amount of capital needed due to exposure to loss. This paper examines this risk measure for “exponential dispersion models”, a wide and popular class of distributions to actuaries which, on one hand, generalizes the Normal and shares some of its many important properties, but on the other hand, contains many distributions of nonnegative random variables like the Gamma and the Inverse Gaussian.

scholarly journals An evaluation and comparison of Value at Risk and Expected Shortfall

2018 ◽  
Vol 15 (4) ◽  
pp. 17-34 ◽  
Author(s):  
Tom Burdorf ◽  
Gary van Vuuren
Keyword(s):  
At Risk ◽  
Monte Carlo ◽  
Emerging Economies ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Expected Shortfall ◽  
Significance Level ◽  
Tail Conditional Expectation ◽  
The Uk

As a risk measure, Value at Risk (VaR) is neither sub-additive nor coherent. These drawbacks have coerced regulatory authorities to introduce and mandate Expected Shortfall (ES) as a mainstream regulatory risk management metric. VaR is, however, still needed to estimate the tail conditional expectation (the ES): the average of losses that are greater than the VaR at a significance level These two risk measures behave quite differently during growth and recession periods in developed and emerging economies. Using equity portfolios assembled from securities of the banking and retail sectors in the UK and South Africa, historical, variance-covariance and Monte Carlo approaches are used to determine VaR (and hence ES). The results are back-tested and compared, and normality assumptions are tested. Key findings are that the results of the variance covariance and the Monte Carlo approach are more consistent in all environments in comparison to the historical outcomes regardless of the equity portfolio regarded. The industries and periods analysed influenced the accuracy of the risk measures; the different economies did not.

CONFIDENCE INTERVALS OF THE ADJUSTED TAIL CONDITIONAL EXPECTATION RISK MEASURE FOR A STATIONARY SERIE

2021 ◽  
Vol 10 (11) ◽  
pp. 3395-3408
Author(s):  
M.T. Fawzi ◽  
O. Hakim ◽  
H. Nacera
Keyword(s):  
Asymptotic Normality ◽  
Confidence Intervals ◽  
Simulation Study ◽  
Conditional Expectation ◽  
Extreme Values ◽  
Risk Measure ◽  
Tail Conditional Expectation

In this paper we present a semi-parametric estimator of the adjusted tail conditional expectation risk measure based on the theory of extreme values for a stationary serie. We prove its asymptotic normality and we construct the confidence intervals. The accuracy of these intervals is evaluated through a simulation study.

TAIL CONDITIONAL EXPECTATIONS FOR GENERALIZED SKEW-ELLIPTICAL DISTRIBUTIONS

2021 ◽  
pp. 1-14
Author(s):  
Baishuai Zuo ◽  
Chuancun Yin
Keyword(s):  
Conditional Expectation ◽  
Elliptical Distributions ◽  
Tail Conditional Expectation ◽  
Conditional Expectations ◽  
Special Cases ◽  
Skew Normal

This paper deals with the multivariate tail conditional expectation (MTCE) for generalized skew-elliptical distributions. We present tail conditional expectation for univariate generalized skew-elliptical distributions and MTCE for generalized skew-elliptical distributions. There are many special cases for generalized skew-elliptical distributions, such as generalized skew-normal, generalized skew Student-t, generalized skew-logistic and generalized skew-Laplace distributions.

OPTIMAL REINSURANCE FROM THE VIEWPOINTS OF BOTH AN INSURER AND A REINSURER UNDER THE CVAR RISK MEASURE AND VAJDA CONDITION

2021 ◽  
pp. 1-29
Author(s):  
Yanhong Chen
Keyword(s):  
Loss Function ◽  
Value At Risk ◽  
Numerical Study ◽  
Risk Measure ◽  
Convex Combination ◽  
Weighting Factor ◽  
Loss Functions ◽  
Conditional Value At Risk ◽  
Optimal Reinsurance ◽  
The Impact

ABSTRACT In this paper, we study the optimal reinsurance contracts that minimize the convex combination of the Conditional Value-at-Risk (CVaR) of the insurer’s loss and the reinsurer’s loss over the class of ceded loss functions such that the retained loss function is increasing and the ceded loss function satisfies Vajda condition. Among a general class of reinsurance premium principles that satisfy the properties of risk loading and convex order preserving, the optimal solutions are obtained. Our results show that the optimal ceded loss functions are in the form of five interconnected segments for general reinsurance premium principles, and they can be further simplified to four interconnected segments if more properties are added to reinsurance premium principles. Finally, we derive optimal parameters for the expected value premium principle and give a numerical study to analyze the impact of the weighting factor on the optimal reinsurance.

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