Large Sample Behavior of the CTE and VaR Estimators under Importance Sampling

Abstract

The α-level value at risk (Var) and the α-level conditional tail expectation (CTE) of a continuous random variable X are defined as its α-level quantile (denoted by q_α ) and its conditional expectation given the event {X > q_α }, respectively. Var is a popular risk measure in the banking sector, for both external and internal reporting purposes, while the CTE has recently become the risk measure of choice for insurance regulation in North America. Estimation of the CTE for company assets and liabilities is becoming an important actuarial exercise, and the size and complexity of these liabilities make inference procedures with good small sample performance very desirable. A common situation is one in which the CTE of the portfolio loss is estimated using simulated values, and in such situations use of variance reduction techniques such as importance sampling have proved to be fruitful. Construction of confidence intervals for the CTE relies on the availability of the asymptotic distribution of the normalized CTE estimator, and although such a result has been available to actuaries, it has so far been supported only by heuristics. The main goal of this paper is to provide an honest theorem establishing the convergence of the normalized CTE estimator under importance sampling to a normal distribution. In the process, we also provide a similar result for the Var estimator under importance sampling, which improves upon an earlier result. Also, through examples we motivate the practical need for such theoretical results and include simulation studies to lend insight into the sample sizes at which these asymptotic results become meaningful.     

Modeling with Weibull-Pareto Models

Abstract

In this paper we develop several composite Weibull-Pareto models and suggest their use to model loss payments and other forms of actuarial data. These models all comprise a Weibull distribution up to a threshold point, and some form of Pareto distribution thereafter. They are similar in spirit to some composite lognormal-Pareto models that have previously been considered in the literature. All of these models are applied, and their performance compared, in the context of a real-world fire insurance data set.     

Consumer and Market Responses to Mad Cow Disease

We examine how consumers and financial markets in the United States reacted to two health warnings about mad cow disease: the first discovery of an infected cow in December 2003 and an Oprah Winfrey show that aired seven years earlier on the potentially harmful effects of mad cow disease. We find a pronounced and significant reduction in beef sales following the first discovery of an infected cow in a product-level scanner data set of a national grocery chain. Cattle futures show a pattern of abnormal price drops comparable to the scanner data. Contracts with longer maturity show smaller drops, suggesting that the market anticipated the impact to be transitory. Cattle futures show abnormal price drops after the Oprah Winfrey show that are more than 50% of the drop following the 2003 discovery of an infected cow.     

Evaluating training effectiveness in India: Exploring the relationship between training components,metacognition and learning outcomes

This study aims to examine the key training factors that significantly impact the learning outcomes of trainees. A comprehensive framework is proposed to investigate the interrelationships among various training components, trainer performance, training usefulness, and their effects on metacognition and learning. Empirical testing of the model is conducted using the partial least squares structural equation modelling approach, analyzing data collected from 322 public servants in North India. The findings reveal that almost all the focal factors comprising a training programme, such as the usefulness of training, trainer performance and metacognition, positively influence trainees' learning. While training agencies should consider all components of the training programme, the perceived usefulness, trainer performance and trainees' metacognition are particularly influential factors in facilitating learning. Training components and trainer performance predict the usefulness of training. This study integrates all focal factors of a training programme into a comprehensive framework using employee data, explaining a significant portion (45%–64%) of the variance in trainees' learning. These findings emphasize the importance of addressing these focal factors thoughtfully when designing and implementing effective training programmes.     

The comparative performance of chartered accountancy students in South Africa: The impact of historical legacies

African students continue to underperform in South Africa's schools and universities. This paper investigates the comparative performance of African chartered accountancy students from school to post-university level. The paper employed a mixed-method approach to analyse a series of cross-sectional datasets. The results showed that African students have underperformed at school, university and at post-university level, although the performance gap appears to be narrowing in the first professional chartered accountancy examination. The differential performance of these students was explained by poorer marks in mathematics and English that can be traced back to historical legacies in the education sector. South African universities, moreover, perpetuate this disadvantage because they have retained Eurocentric teaching approaches. In order to remove these barriers, tuition at school and university must be complemented by cross-cultural teaching practices and bridging programmes.