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.

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.

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.

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.

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.

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.

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.

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