Market Price of Insurance Risk Implied by Catastrophe Derivatives

Abstract

Insurance derivatives facilitate the trading of insurance risks on capital markets, such as catastrophe derivatives that were traded on the Chicago Board of Trade. Simultaneously, insurance risks are traded through reinsurance portfolios. In this paper we make inferences about the market price of risk implied by the information embedded in the prices of these two assets.     

Credibility for Severity Revisited

Abstract

It is basic actuarial knowledge that the pure premium of an insurance contract can be written as the product of the expected claim number and the expected claim amount. Actuaries use credibility theory to incorporate the contract’s individual experience into this calculation in a statistically optimal way. For many years, however, the use of credibility was limited to the frequency component. Starting with the paper by Hewitt (1971), there have been various suggestions as to how credibility theory also can be applied to the severity component of the pure premium. The latest such suggestion, Frees (2003), revived the interest in the problem.

In this paper, we review four different formulas incorporating frequency and severity into credibility calculations. We then compare by simulation which one is most accurate at predicting a contract’s next-year outcome. It is found that the classical formula of Bühlmann (1967) is as good as the other ones in many cases. Alternatives, however, may offer easier analysis of the separate effects of frequency and severity on the premium.

We also show that all the formulas reviewed in this paper stem from the same minimization problem, and we present a general, integrated, solution. At the same time, we complete Gerber (1972) by providing a proof to the main result of this paper and by stating required additional assumptions.     

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.     

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.