One of the pricing strategies for Bonus–Malus (BM) systems relies on the decomposition of the claims’ randomness into one part accounting for claims’ frequency and the other part for claims’ severity. By mixing an exponential with a Lévy distribution, we focus on modelling the claim severity component as a Weibull distribution. For a Negative Binomial number of claims, we employ the Bayesian approach to derive the BM premiums for Weibull severities. We then conclude by comparing our explicit formulas and numerical results with those for Pareto severities that were introduced by Frangos & Vrontos.

The operation of monetary policy is likely to affect securities markets and asset values. This is of relevance to actuaries who work in or advise non-bank financial institutions such as pension funds and insurance companies. This paper examines different theories of monetary policy and the relationship between monetary policy and asset prices. It is found that central bank models have, at least until recently, tended to sideline consideration of the transmission of monetary policy through asset markets but that, with the implementation of quantitative easing, it is a subject that cannot be ignored. Many monetary schools, in fact, suggest that asset markets can be significantly affected by changes to monetary policy and those schools have lessons for important aspects of actuarial theory and practice.

We develop a generalisation of the World Bank (1994) model of forced saving for retirement. This broader model consists of two tiers of second pillar savings – mandated and non-mandated (voluntary). Furthermore, the government can set two types of guarantees on the first (mandated) tier – investment returns and annuity prices – leading to possible cross-subsidisation between the tiers. This has the potential to induce social redistribution, foster a liquid private market for life annuities, and obviate some of the investment risk and annuity price risk that retirees face.

We formulate a quantitative model of financial flows within such a system, which explains the mechanism by which cross-subsidisation occurs. Based on this analysis, a taxonomy of two-tiered retirement systems is presented, that is based on the choices that the government makes.

This paper explores how we can apply various modern data mining techniques to better understand Australian Income Protection Insurance (IPI). We provide a fast and objective method of scoring claims into different portfolios using available rating factors. Results from fitting several prediction models are compared based on not only the conventional loss prediction error function, but also a modified loss function. We demonstrate that the prediction power of all the data mining methods under consideration is clearly evident using a misclassification plot. We also point out that this predictability can be masked by looking at just the conventional prediction error function. We then suggest using the stepwise regression technique to reduce the number of variables used in the data mining methods. Apart from this variable selection method, we also look at principal components analysis to increase understanding of the rating factors that drive claim durations of insured lives. We also discuss and compare how different variable combining techniques can be used to weight available predicting variables. One interesting outcome we discover is that principal components analysis and the weighted combination prediction model together provide very consistent results on identifying the most significant variables for explaining claim durations.

Crop index microinsurance is a novel product that has been piloted and implemented in many developing countries. We attempt to give an overview of crop index microinsurance, covering the major issues needed to design, price and implement a crop index microinurance programme. In some ways, providing insurance to the poor is fundamentally different to providing insurance to the middle-income or rich; in other ways, including in the actuarial fields of product design, pricing and risk financing, there are strong similarities. We offer a stylised discussion of these differences and similarities, with particular reference to issues of potential interest to actuaries, and propose an actuarial framework for crop index microinsurance. Case studies from Malawi and the Philippines provide examples for what does and what does not seem to work in crop index microinsurance, and motivation for further work needed.

In this paper, we investigate the density function of the time of ruin in the classical risk model with a constant dividend barrier. When claims are exponentially distributed, we derive explicit expressions for the density function of the time of ruin and its decompositions: the density of the time of ruin without dividend payments and the density of the time of ruin with dividend payments. These densities are obtained based on their Laplace transforms, and expressed in terms of some special functions which are computationally tractable. The Laplace transforms are being inverted using a magnificent tool, the Lagrange inverse formula, developed in Dickson and Willmot (2005). Several numerical examples are given to illustrate our results.

Matrix-form Poisson probability distributions were recently introduced as one matrix generalization of Panjer distributions. We show in this paper that under the constraint that their representation is to be nonnegative, they have a physical interpretation as extensions of PH distributions, and we name this restricted family Phase-type Poisson. We use our physical interpretation to construct an EM algorithm-based estimation procedure.

We compare quantitatively six simulation strategies for mortality projection with the Poisson Lee–Carter model. We test these strategies on New Zealand mortality data and discuss the simulated results of the mortality index, death rates, and life expectancy.

This paper develops a term structure model for the UK nominal, real and implied inflation spot zero-coupon rates simultaneously. We start with fitting a descriptive yield curve model proposed by Cairns (1998) to fill the missing values for certain given days at certain maturities in the yield curve data provided by the Bank of England. We compare four different fixed ‘exponential rate’ parameter sets and decide the set of parameters which fits the data best. With the chosen set of parameters we fit the Cairns model to the daily values of the term structures. By applying principal component analysis on the hybrid data (Bank of England data and fitted spot rates for the missing values) we find three principal components, which can be described as ‘level’, ‘slope’ and ‘curvature’, for each of these series. We explore the relation between these principal components to construct a ‘yield-only’ model for actuarial applications. Main contribution of this paper is that the models developed in the paper enable the practitioners to forecast three term structures simultaneously and it also provides the forecast for whole term structures rather than just short and long end of the yield curves.

Risk aggregation is a popular method used to estimate the sum of a collection of financial assets or events, where each asset or event is modelled as a random variable. Applications include insurance, operational risk, stress testing and sensitivity analysis. In practice, the sum of a set of random variables involves the use of two well-known mathematical operations: n-fold convolution (for a fixed number n) and N-fold convolution, defined as the compound sum of a frequency distribution N and a severity distribution, where the number of constant n-fold convolutions is determined by N, where the severity and frequency variables are independent, and continuous, currently numerical solutions such as, Panjer’s recursion, fast Fourier transforms and Monte Carlo simulation produce acceptable results. However, they have not been designed to cope with new modelling challenges that require hybrid models containing discrete explanatory (regime switching) variables or where discrete and continuous variables are inter-dependent and may influence the severity and frequency in complex, non-linear, ways. This paper describes a Bayesian Factorisation and Elimination (BFE) algorithm that performs convolution on the hybrid models required to aggregate risk in the presence of causal dependencies. This algorithm exploits a number of advances from the field of Bayesian Networks, covering methods to approximate statistical and conditionally deterministic functions to factorise multivariate distributions for efficient computation. Experiments show that BFE is as accurate on conventional problems as competing methods. For more difficult hybrid problems BFE can provide a more general solution that the others cannot offer. In addition, the BFE approach can be easily extended to perform deconvolution for the purposes of stress testing and sensitivity analysis in a way that competing methods do not.

This is the first of two papers in which we estimate transition probabilities amongst levels of disability as defined in the Australian Survey of Disability, Ageing and Carers. In this paper we describe both the main tools of our estimation and the estimation of the numbers of individuals in different disability categories at annual intervals using survey data that are available at five year intervals. In Paper II we describe our estimation procedure, followed by its implementation, discussion of results and graduation of the estimated transition probabilities.

We construct yield curve models for the UK nominal, real and implied inflation spot rates considering the linkage between their term structures and some macroeconomic variables, in particular, realised inflation and real GDP growth. The paper extends the benchmark “yield-only” model proposed by Şahin et al. (2014) by exploring the bidirectional relations between the yield curve factors and the macroeconomic variables and proposes a “yield-macro” model. Although a simple autoregressive order one process fits the yield curve factors quite well the insertion of some macroeconomic variables such as realised inflation and real GDP growth improves the models significantly. We also model macroeconomic variables that take the term structures into account and compare the yield-macro model with Wilkie’s model both philosophically and empirically.

This is the second of two papers in which we estimate transition probabilities amongst levels of disability as defined in the Australian Survey of Disability, Ageing and Carers. In this paper we describe our estimation procedure, followed by its implementation, discussion of results and graduation of the estimated transition probabilities.

The claims development result (CDR) is the difference between the best estimate predictions of the ultimate claim in 2 successive years. With best estimate reserves it is often argued that CDR’s in consecutive years should fluctuate randomly around zero. However, in practice one frequently observes that CDR’s in a given line of business have the same sign over several consecutive years. We show that this is a phenomenon which is not unusual and to be expected in situations of change. Moreover, we show how situations of change can adequately be described by a model, taking into account the evolving external information.

In this paper, the first study of stochastic economic modelling with Chinese data is conducted for actuarial use. Univariate models, vector autoregression and two cascade systems (equity-driving cascade system and price-inflation-driving cascade system) are described and compared. We focus on six major economic assumptions for modelling purposes, which are price inflation rate, wage inflation rate, long-term interest rate, short-term interest rate, equity total return and bond total return. Granger causality tests are used to identify the driving force of a cascade system. Robust standard errors are estimated for each model. Diagnostic checking of residuals, goodness-of-fit measures and out-of-sample validations are applied for model selection. By comparing different models for each variable, we find that the equity-driving cascade system is the best structure for actuarial use in China. The forecasts of the variables could be applied as economic inputs to stochastic projection models of insurance portfolios or pension funds for short-term asset and liability cash flow forecasting.

Single copies of the papers listed here can be obtained, subject to charge and copyright regulations, from the libraries of the Institute and Faculty of Actuaries. Members can also access the journals online by registering for the libraries’ Athens service. Email: libraries@actuaries.org.uk or telephone 0131 240 1311 or 020 7632 2114 for a password.

Single copies of all the papers listed here can be obtained, subject to charge and copyright regulations, from the actuarial profession's libraries. Issues may be borrowed by members. Tel: 0131 240 1311 or 020 7632 2114; libraries@actuaries.org.uk