During the past decade many insurance solvency standards have introduced a requirement to use premium liabilities and diversified risk margins. With the introduction of IFRS 4, most countries' accounting standards augmented unearned premium provisions with premium liabilities. Many countries' accounting standards have also required the inclusion of diversified risk margins in premium liability provisions. Calculating diversified risk margins requires estimates, correlations and variances of the outstanding claims and premium liabilities. This paper shows how the application of a random effects model to claims payments can be used to unify the estimation of outstanding claims provisions and premium liability provisions, including the estimation of correlations between outstanding claims and premium liability. Estimators are proposed for the model parameters. While the model parameters are estimated using aggregated historical data, the model applies to individual claims, because premium liabilities are a subset of each data point in the aggregate data given in claims triangles, and thus an individual claim model is required to obtain the scaling of mean and variance.
We drive our cars too much because our motor insurance costs are a fixed cost per annum, unrelated to how far we actually drive. By driving our cars too much we all end up worse off from problems such as more accidents, pollution, traffic congestion, global warming etc. This paper presents a better approach to insurance.
One way to understand competitor premium rates is to use the brute force technique - to obtain enough competitor quotes to fully reverse engineer their pricing structure. But the brute force approach has practical problems, including speed and legality. this paper suggests a more intelligent approach.
Compulsory third party motor insurance (CTP) is a highly regulated insurance environment. It provides insurers with a unique opportunity to operate in a large and transparent market. In such a market environment, insurers must understand the rules and understand their competitors’ behaviour in order to determine their optimal strategy. This paper applies the rules of game theory to explain the dynamics of Australia's CTP markets.
This paper was an entry for the Brian Hey Prize in 2000 in the UK. It introduces the concept and mathematics of regime switching models, and then applies them to insurance cycles to quantify their characteristics.
This paper was presented at the IAA General Insurance Seminar in 2001. It is a non technical introduction to regime switching models and their advantages over commonly used time series techniques when applied to many economic and insurance situations.
This paper was presented at the ICAAF conference in Hong Kong in 2002. It uses some standard tests for mean reversionary behaviour, and derives some new statistical tests. These tests are applied to the official cash rates in Australia and NZ. Finally, an alternative to mean reversion is proposed.
Actuaries, as managers of risk, come across correlations daily. But sometimes correlations are misleading, and sometimes we need more. This paper covers the fundamentals of correlations and extends the correlation concept to copula. It also proposes a new empirical measure of tail dependence. This topic is the basis for understanding why the capital asset pricing model is not applicable for setting insurance premium levels.
DFA models can be likened to computer imaging techniques such as rendering. They both involve complex calculations that take a considerable amount of CPU time. This paper looks at some techniques to provide higher resolution DFA pictures, such as Latin Hypercube sampling, low discrepancy sequences, parallel processing, using aggregate distributions, avoiding correlations and avoiding unnecessary calculations.
This was Colin's first research paper, presented at the IAA General Insurance Seminar in 1994. It revolutionised the monitoring of the adequacy of insurance premiums. This paper was prompted by the effect of substantial increases in property catastrophe reinsurance costs during the early 1990s. After demonstrating that conventional insurance performance measures will fail during periods of rapid increases in the cost of reinsurance, the paper proposes a more robust and intuitive set of performance measures.
This paper, presented at the IAA General Insurance Seminar in 1995, looks at the effectiveness of different profit targets used by general insurers to set premium levels. It also looks at the historical relationship between insurance profits against interest rates and share returns.
As the guest speaker of a joint meeting of The Statistical Society of Australia (NSW Branch) and the Illawarra Statistics Group in July 2003, Colin chose to present some of the innovative approaches in time series analysis and time series models that he has found necessary for designing value-at-risk models. In real life many commodities do not behave like the mainstream theoretical models because they are too thinly traded, and they have stronger tail dependence than would be expected from their correlation coefficients.