In this paper the authors conduct an asymptotic analysis of the exact bootstrap bias correction for the empirical Conditional Tail Expectation, focusing on its performance as a point estimator of the bias of the empirical CTE.

This study note focuses on actuarial applications and loss distributions for insurance products.

In this paper the authors provide an honest theorem establishing the convergence of the normalized conditional tail expectation [CTE] estimator under importance sampling to a normal distribution. In the process, they also provide a similar result for the value at risk [VaR] estimator under importance sampling, which improves upon an earlier result.

In this article the authors derive explicit formulas of the Conditional Tail Expectation and higher moments for the univariate exponential family class, which extends the natural exponential family, using the canonical representation.

A common characteristic for many insurance risks is the right-tail risk, representing low-frequency, large-loss events. In this paper I propose a measure of the right-tail risk by defining the right-tail deviation and the right-tail index. I explain how the right-tail deviation measures the right-tail risk and compare it to traditional measures such as standard deviation, the Gini mean, and the expected policyholder deficit. The right-tail index is applied to some common parametric families of loss distributions.

Discusses various approaches for measuring tail risk and how to price for tail risk using capital market consistent techniques. Session # 2 PD of the Sept. 2010 Valuation Actuary Symposium in Chicago.

Discusses various approaches for measuring tail risk and how to price for tail risk using capital market consistent techniques. Session # 2 PD of the Sept. 2010 Valuation Actuary Symposium in Chicago.

Presentation from the 2007 SOA Annual Meeting that was moderated by Mr. Heins. Discusses stochastic modeling for long-term care and principles based reserving.

The purpose of this article is to provide a high level summary of the paper “Variance of the CTE Estimator” by B. John Manistre and Geoffrey H. Hancock that appeared in the North American Actuarial Journal in 2005. The authors also expanded on some of the results.

This paper discusses a natural and convenient statistic, the nested L-statistic, investigates its performance using a simulation study, and considers an example involving the comparison of risk measure values where the risks of interest are those associated with tornado damage in different time periods and different regions. From the Actuarial Research Clearing House, 2008, Vol.1.