In this paper, we consider a number of practical and theoretical aspects of the Wilkie asset model, many of which apply to any similar model used for simulation over time. We discuss the experience of the Wilkie model since 2009. We then discuss the variables that can form the working set, the input set and the output set, all of which may be different. There are different ways of simulating, either in a linear parallel structure or in a branching tree structure. We then discuss the initial conditions required, which may be market conditions at some date, or may be “neutral” initial conditions, which may be defined in different ways. One method of generating initial conditions would be to simulate them randomly, from their own long-term distribution, and we show how to calculate the means, variances and covariances of these. What we call “neutralising parameters” may have a role, and we discuss how these may be found. Finally, we suggest using additional information in the first periods of the simulation to adjust the formulae or parameters for a limited “select period”.

In this paper, we revisit the determination of optimal relativities under the linear form of relativities that is more viable in designing a commercial bonus-malus system. We derive the analytical formulae for the optimal linear relativities subject to a financial balanced inequality constraint. We also numerically investigate the impact of different a priori risk classification towards the effectiveness of transition rules. Our results show that the a priori risk segmentation is not a sensitive factor for the effectiveness of transition rules. Furthermore, relative to the general relativities, we find that the restriction of linear relativities only produces a small amount of deterioration towards the numerical value of the optimised objective function.

We apply methods from multiple attribute decision making (MADM) to the problem of selecting an optimal reinsurance level. In particular, we apply the Technique for Order of Preference by Similarity to Ideal Solution method with Mahalanobis distance. We consider the classical risk model under a reinsurance arrangement – either excess of loss or proportional – and we consider scenarios that have the same finite time ruin probability. For each of these scenarios we calculate three quantities: released capital, expected profit and expected utility of resulting wealth. Using these inputs, we apply MADM to find optimal retention levels. We compare and contrast our findings with those when decisions are based on a single attribute.

The class of spectrally positive Lévy processes is a frequent choice for modelling loss processes in areas such as insurance or operational risk. Dependence between such processes (e.g. between different lines of business) can be modelled with Lévy copulas. This approach is a parsimonious, efficient and flexible method which provides many of the advantages akin to distributional copulas for random variables. Literature on Lévy copulas seems to have primarily focussed on bivariate processes. When multivariate settings are considered, these usually exhibit an exchangeable dependence structure (whereby all subset of the processes have an identical marginal Lévy copula). In reality, losses are not always associated in an identical way, and models allowing for non-exchangeable dependence patterns are needed. In this paper, we present an approach which enables the development of such models. Inspired by ideas and techniques from the distributional copula literature we investigate the procedure of nesting Archimedean Lévy copulas. We provide a detailed analysis of this construction, and derive conditions under which valid multivariate (nested) Lévy copulas are obtained. Our results are discussed and illustrated, notably with an example of model fitting to data.

These abstracts are compiled by the library service of the Institute and Faculty of Actuaries. Single copies of the papers listed here can be obtained, subject to copyright law, by contacting the libraries. There may be a charge for this service. Members of the Institute and Faculty of Actuaries can also access these journals directly by registering for the eLibrary. A password is available on request. Please email [email protected] for more information.