This paper presents pricing innovations to German car insurance. The purpose is to provide an effective approach to adapting actuarial pricing decision to incorporate telematic data, which differs substantially from established tariff criteria in complexity and volume. A vehicle mobility model and a real-world sample of driving profiles form the input into the analysis. We propose an allocation of the driving profiles based on velocity and acceleration parameters to specific driving styles for evaluating the driving behaviour to subsequently enable discounts or surcharges on the premiums to obtain usage-based insurance premiums. The result is highly relevant for actuaries, who calculate the tariffs, but also for managers, as they have to make a pricing decision.

A non-parametric test based on nested L-statistics and designed to compare the riskiness of portfolios was introduced by Brazauskas et al. (2007). Its asymptotic and small-sample properties were primarily explored for independent portfolios, though independence is not a required condition for the test to work. In this paper, we investigate how performance of the test changes when insurance portfolios are dependent. To achieve that goal, we perform a simulation study where we consider three different risk measures: conditional tail expectation, proportional hazards transform, and mean. Further, three portfolios are generated from exponential, Pareto, and lognormal distributions, and their interdependence is modelled with the three-dimensional t and Gaussian copulas. It is found that the presence of strong positive dependence (comonotonicity) makes the test very liberal for all the risk measures under consideration. For types of dependence that are more common in an insurance environment, the effect of dependence is less dramatic but the results are mixed, i.e., they depend on the chosen risk measure, sample size, and even on the test’s significance level. Finally, we illustrate how to incorporate such findings into sensitivity analysis of the decisions. The risks we analyse represent tornado damages in different regions of the United States from 1890 to 1999.

This paper outlines a framework for explicitly including ethics in actuarial education. The framework includes integrity, the cardinal virtues (justice, prudence, self-control and courage), and vocation. It is based on a traditional understanding of ethics, and it is argued that it has the potential to be widely acceptable. Justification, from philosophy, is found mainly in virtue ethics, and the work of Alasdair MacIntyre. The framework is concerned with matters of character as well as behaviour and ultimate outcomes (which are the respective concerns of apparently competing deontological and teleological theories). Integrity and the cardinal virtues can be found within current professional standards or, it is argued in the case of courage, should be there. We come to appreciate and display the virtues as we are inducted into a professional community by teachers and mentors. Our view of ethics is incomplete, however, without acknowledgement of our own weaknesses and failures, and an understanding of the role of regulation. Such understanding should include insight into the way in which ideologies and institutions can pervert ethics for the benefit of vested interests. Finally, suggestions are made as to how the framework of the virtues can be included in the actuarial syllabuses.

A deep-deferred annuity is a deferred annuity where payments start very late in life, i.e. well after the normal retirement age. This annuity has received much attention lately as it was made accessible to 401(k) plans in the United States in 2014. By transferring the risk of outliving retirement savings at high ages to annuity providers, deep-deferred annuities provide annuitants with enhanced later-life financial security. However, the valuation of this annuity suffers from high uncertainty because the mortality data at high ages are sparse and possibly unreliable. In this paper, we use risk ratio to measure demographic risk in the valuation. Demographic risk is decomposed into the following four components: (1) mortality tail curve risk, (2) mortality improvement model risk, (3) parameter risk in mortality tail curves, and (4) parameter risk in mortality improvement rate models. Our quantitative analysis aims to provide insights into the development and risk management of deep-deferred annuities.

This paper explores the characteristics of 2,141 operational risk events amongst European (EU) and US banks over the period 2008–2014. We have analysed the operational risk events using a method originating in biology for the study of interrelatedness of characteristics in a complex adaptive system. The methodology, called cladistics, provides insights into the relationships between characteristics of operational risk events in banks that is not available from the traditional statistical analysis. We have used cladistics to explore if there are consistent patterns of operational risk characteristics across banks in single and different geographic zones. One significant pattern emerged which indicates there are key, stable characteristics across both geographic zones and across banks in each zone. The results identify the characteristics that could then be managed by the banks to reduce operational risk losses. We also have analysed separately the characteristics of operational risk events for “big” banks and extreme events and these results indicate that big banks and small banks have similar key operational risk characteristics, but the characteristics of extreme operational risk events are different to those for the non-extreme events.

This paper explores and develops alternative statistical representations and estimation approaches for dynamic mortality models. The framework we adopt is to reinterpret popular mortality models such as the Lee–Carter class of models in a general state-space modelling methodology, which allows modelling, estimation and forecasting of mortality under a unified framework. We propose alternative model identification constraints which are more suited to statistical inference in filtering and parameter estimation. We then develop a class of Bayesian state-space models which incorporate a priori beliefs about the mortality model characteristics as well as for more flexible and appropriate assumptions relating to heteroscedasticity that present in observed mortality data. To study long-term mortality dynamics, we introduce stochastic volatility to the period effect. The estimation of the resulting stochastic volatility model of mortality is performed using a recent class of Monte Carlo procedure known as the class of particle Markov chain Monte Carlo methods. We illustrate the framework using Danish male mortality data, and show that incorporating heteroscedasticity and stochastic volatility markedly improves model fit despite an increase of model complexity. Forecasting properties of the enhanced models are examined with long-term and short-term calibration periods on the reconstruction of life tables.

In this paper we analyse insurance claim frequency data using the bivariate negative binomial regression (BNBR) model. We use general insurance data on claims from simple third-party liability insurance and comprehensive insurance. We find that bivariate regression, with its capacity for modelling correlation between the two observed claim counts, provides both a superior fit and out-of-sample prediction compared with the more common practice of fitting univariate negative binomial regression models separately to each claim type. Noting the complexity of BNBR models and their potential for a large number of parameters, we explore the use of model shrinkage methodology, namely the least absolute shrinkage and selection operator (Lasso) and ridge regression. We find that models estimated using shrinkage methods outperform the ordinary likelihood-based models when being used to make predictions out-of-sample. We find that the Lasso performs better than ridge regression as a method of shrinkage.

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