It is a great honor for me to have been appointed to the new Editor-in-Chief (EiC) of ASTIN Bulletin. I have been serving as Editor for ASTIN Bulletin under the retiring EiC Andrew Cairns since 2011. Andrew Cairns has been EiC of ASTIN Bulletin for 17 years, the first 5 years together with Paul Embrechts, another 2 years jointly with Shaun Wang, and since 2008 he has been solely responsible for ASTIN Bulletin. Andrew Cairns has done an extraordinary job; with his huge commitment and knowledge, he has established ASTIN Bulletin as the leading journal in actuarial science, both in industry and academia. In his time, ASTIN Bulletin has been awarded the Thomson Reuters Impact Factor, it has changed the publisher to Cambridge University Press, and it has integrated all of the scientific sections of the International Actuarial Association IAA. Today, ASTIN Bulletin publishes roughly 30 articles per year (with an average acceptance rate for new submissions of about 30%). Our greatest thanks go to Andrew Cairns for his achievements and this great success of ASTIN Bulletin.

Gunnar Benktander passed away on February 25, 2018 at the age of 99. He left his family, and also the actuarial (non-life) community, after a long and very full life.

This article proposes a neural-network approach to predict and simulate human mortality rates. This semi-parametric model is capable to detect and duplicate non-linearities observed in the evolution of log-forces of mortality. The method proceeds in two steps. During the first stage, a neural-network-based generalization of the principal component analysis summarizes the information carried by the surface of log-mortality rates in a small number of latent factors. In the second step, these latent factors are forecast with an econometric model. The term structure of log-forces of mortality is next reconstructed by an inverse transformation. The neural analyzer is adjusted to French, UK and US mortality rates, over the period 1946–2000 and validated with data from 2001 to 2014. Numerical experiments reveal that the neural approach has an excellent predictive power, compared to the Lee–Carter model with and without cohort effects.

Although loss reserving has been deeply studied in the literature, there are still practical issues that have not been addressed a lot. One of them is the estimation of reserves during the year, which is necessary for forecasts or closings during the year. We will study the following question: What can be done for forecasts and closings during the year that goes along with the reserving at year end? In order to make it not too complicated, we will focus on the Chain-Ladder method introduced by Mack (1993). We will describe several methods that are used in practice. We will discuss advantages and disadvantages of these methods based on a simple deterministic example. Roughly spoken, we will see that you may shift development or accident periods, or may split development periods, but should not split accident periods.

Actuarial risk classification studies are typically confined to univariate, policy-based analyses: Individual claim frequencies are modelled for a single product, without accounting for the interactions between the different coverages bought by the members of the same household. Now that large amounts of data are available and that the customer's value is at the heart of insurers' strategies, it becomes essential to develop multivariate risk models combining all the products subscribed by the members of the household in order to capture the correlation effects. This paper aims to supplement the standard actuarial policy-based approach with a household-based approach. This makes the actuarial model more complex but also increases the volume of available information which eases and refines forecasting. Possible cross-selling opportunities can also be identified.

We consider a modification to the Poisson common factor model and utilise a generalised linear model (GLM) framework that incorporates a smoothing process and a set of linear constraints. We extend the standard GLM model structure to adopt Lagrange methods and P-splines such that smoothing and constraints are applied simultaneously as the parameters are estimated. Our results on Australian, Canadian and Norwegian data show that this modification results in an improvement in mortality projection in terms of producing more accurate forecasts in the out-of-sample testing. At the same time, projected male-to-female ratio of death rates at each age converges to a constant and the residuals of the models are sufficiently random, indicating that the use of smoothing does not adversely affect the fit of the model. Further, the irregular patterns in the estimates of the age-specific parameters are moderated as a result of smoothing and this model can be used to produce more regular projected life tables for pricing purposes.

We consider a Tweedie's compound Poisson regression model with fixed and random effects, to describe the payment numbers and the incremental payments, jointly, in claims reserving. The parameter estimates are obtained within the framework of hierarchical generalized linear models, by applying the h-likelihood approach. Regression structures are allowed for the means and also for the dispersions. Predictions and prediction errors of the claims reserves are evaluated. Through the parameters of the distributions of the random effects, some external information (e.g. a development pattern of industry wide-data) can be incorporated into the model. A numerical example shows the impact of external data on the reserve and prediction error evaluations.

In a risk exchange, participants trade a privately owned risk for a share in a pool. If participants agree on a valuation rule, it can be decided whether or not, according to the given rule, these trades take place at equal value. If equality of values holds for all participants, then the exchange is said to be “financially fair”. It has been shown by Bühlmann and Jewell (1979) that, under mild assumptions, the constraint of financial fairness singles out a unique solution among the set of all Pareto efficient risk exchanges. In this paper, we find that an analogous statement is true if we limit ourselves to linear exchanges. Conditions are provided for existence and uniqueness of linear sharing rules that are both financially fair and Pareto efficient among all linear sharing rules. The performance of the linear rule is compared to that of the general (nonlinear) rule in a number of specific cases.

Recently, there has been an increasing interest from life insurers to assess their portfolios' mortality risks. The new European prudential regulation, namely Solvency II, emphasized the need to use mortality and life tables that best capture and reflect the experienced mortality, and thus policyholders' actual risk profiles, in order to adequately quantify the underlying risk. Therefore, building a mortality table based on the experience of the portfolio is highly recommended and, for this purpose, various approaches have been introduced into actuarial literature. Although such approaches succeed in capturing the main features, it remains difficult to assess the mortality when the underlying portfolio lacks sufficient exposure. In this paper, we propose graduating the mortality curve using an adaptive procedure based on the local likelihood. The latter has the ability to model the mortality patterns even in presence of complex structures and avoids relying on expert opinions. However, such a technique fails to offer a consistent yet regular structure for portfolios with limited deaths. Although the technique borrows the information from the adjacent ages, it is sometimes not sufficient to produce a robust life table. In the presence of such a bias, we propose adjusting the corresponding curve, at the age level, based on a credibility approach. This consists in reviewing the assumption of the mortality curve as new observations arrive. We derive the updating procedure and investigate its benefits of using the latter instead of a sole graduation based on real datasets. Moreover, we look at the divergences in the mortality forecasts generated by the classic credibility approaches including Hardy–Panjer, the Poisson–Gamma model and the Makeham framework on portfolios originating from various French insurance companies.

We discuss the role of integrated chance constraints (ICC) as quantitative risk constraints in asset and liability management (ALM) for pension funds. We define two types of ICC: the one period integrated chance constraint (OICC) and the multiperiod integrated chance constraint (MICC). As their names suggest, the OICC covers only one period, whereas several periods are taken into account with the MICC. A multistage stochastic linear programming model is therefore developed for this purpose and a special mention is paid to the modeling of the MICC. Based on a numerical example, we first analyze the effects of the OICC and the MICC on the optimal decisions (asset allocation and contribution rate) of a pension fund. By definition, the MICC is more restrictive and safer compared to the OICC. Second, we quantify this MICC safety increase. The results show that although the optimal decisions from the OICC and the MICC differ, the total costs are very close, showing that the MICC is definitely a better approach since it is more prudent.

We propose a Bayesian spline model which uses a natural cubic B-spline basis with knots placed at every development period to estimate the unpaid claims. Analogous to the smoothing parameter in a smoothing spline, shrinkage priors are assumed for the coefficients of basis functions. The accident period effect is modeled as a random effect, which facilitate the prediction in a new accident period. For model inference, we use Stan to implement the no-U-turn sampler, an automatically tuned Hamiltonian Monte Carlo. The proposed model is applied to the workers' compensation insurance data in the United States. The lower triangle data is used to validate the model.

In this paper, we study an optimal insurance problem in the presence of background risk from the perspective of an insured with higher-order risk attitudes. We introduce several useful dependence notions to model positive dependence structures between the insurable risk and background risk. Under these dependence structures, we compare insurance contracts of different forms in higher-order risk attitudes and establish the optimality of stop-loss insurance form. We also explicitly derive the optimal retention level. Finally, we carry out a comparative analysis and investigate how the change in the insured's initial wealth or background risk affects the optimal retention level.

A method to hedge variable annuities in the presence of basis risk is developed. A regime-switching model is considered for the dynamics of market assets. The approach is based on a local optimization of risk and is therefore very tractable and flexible. The local optimization criterion is itself optimized to minimize capital requirements associated with the variable annuity policy, the latter being quantified by the Conditional Value-at-Risk (CVaR) risk metric. In comparison to benchmarks, our method is successful in simultaneously reducing capital requirements and increasing profitability. Indeed the proposed local hedging scheme benefits from a higher exposure to equity risk and from time diversification of risk to earn excess return and facilitate the accumulation of capital. A robust version of the hedging strategies addressing model risk and parameter uncertainty is also provided.

Age-period-cohort models used in life and general insurance can be over-parameterized, and actuaries have used several methods to avoid this, such as cubic splines. Regularization is a statistical approach for avoiding over-parameterization, and it can reduce estimation and predictive variances compared to MLE. In Markov Chain Monte Carlo (MCMC) estimation, regularization is accomplished by the use of mean-zero priors, and the degree of parsimony can be optimized by numerically efficient out-of-sample cross-validation. This provides a consistent framework for comparing a variety of regularized MCMC models, such as those built with cubic splines, linear splines (as ours is), and the limiting case of non-regularized estimation. We apply this to the multiple-trend model of Hunt and Blake (2014).

We propose a new parametric model for the modelling and estimation of event distributions for individuals in different firms. The analysis uses panel data and takes into account individual and firm effects in a non-linear model. Non-observable factors are treated as random effects. In our application, the distribution of accidents is affected by observable and non-observable factors from vehicles, drivers and fleets of vehicles. Observable and unobservable factors are significant to explain road accidents, which mean that insurance pricing should take into account all these factors. A fixed effects model is also estimated to test the consistency of the random effects model.

The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf) and the cumulative distribution function (cdf) of aggregated risks, modelled according to a mixture of exponential distributions. We first review the properties of the multivariate mixture of exponential distributions, to then obtain the analytical formulation for the pdf and the cdf for the aggregated distribution. We study in detail some specific families with Pareto (Sarabia et al., 2016), gamma, Weibull and inverse Gaussian mixture of exponentials (Whitmore and Lee, 1991) claims. We also discuss briefly the computation of risk measures, formulas for the ruin probability (Albrecher et al., 2011) and the collective risk model. An extension of the basic model based on mixtures of gamma distributions is proposed, which is one of the suggested directions for future research.

We present a savings plan for retirement that removes risk by fixing a constraint on a life-long pension so that it has an upper and a lower bound. This corresponds to the ideas of Nobel laureate R.C. Merton whose implementation has never been published. We show with an illustration that our proposed practical algorithm reproduces the theoretical results after a savings period of around 30 years by using daily, monthly, weekly or yearly updates of the investment positions. We calculate the percentiles of the final accumulated wealth distribution for the adjusted implementation. In the simulated illustration, we observe that the adjusted values converge to the theoretical values of the percentiles when the frequency of update increases. We conclude that monthly adjustments result in a practical way to implement theoretical results that were obtained under the hypothesis of a continuous process by Donnelly et al. (2015). This method is easy to use in practice by pension savers and fund managers.

We consider a profitable, risky setting with two separate, correlated asset and liability processes (first introduced by Gerber and Shiu, 2003). The company that is considered is allowed to distribute excess profits (traditionally referred to as dividends in the literature), but is regulated and is subject to particular regulatory (solvency) constraints. Because of the bivariate nature of the surplus formulation, such distributions of excess profits can take two alternative forms. These can originate from a reduction of assets (and hence a payment to owners), but also from an increase of liabilities (when these represent the wealth of owners, such as in pension funds). The latter is particularly relevant if distributions of assets do not make sense because of the context, such as in regulated pension funds where assets are locked until retirement. In this paper, we extend the model of Gerber and Shiu (2003) and consider recovery requirements for the distribution of excess funds. Such recovery requirements are an extension of the plain vanilla solvency constraints considered in Paulsen (2003), and require funds to reach a higher level of funding than the solvency level (if and after it is triggered) before excess funds can be distributed again. We obtain closed-form expressions for the expected present value of distributions (asset decrements or liability increments) when a distribution barrier is used.

The paper is concerned with multiple claim arrays. In recognition of the extensive use by practitioners of large correlation matrices for the estimation of diversification benefits in capital modelling, we develop a methodology for the construction of such correlation structures (to any dimension). Indeed, the literature does not document any methodology by which practitioners, who often parameterise those correlations by means of informed guesswork, may do so in a disciplined and parsimonious manner.

We construct a broad and flexible family of models, where dependency is induced by common shock components. Models incorporate dependencies between observations both within arrays and between arrays. Arrays are of general shape (possibly with holes), but include the usual cases of claim triangles and trapezia that appear in the literature. General forms of dependency are considered with cell-, row-, column-, diagonal-wise, and other forms of dependency as special cases. Substantial effort is applied to practical interpretation of such matrices generated by the models constructed here.

Reasonably realistic examples are examined, in which an expression is obtained for the general entry in the correlation matrix in terms of a limited set of parameters, each of which has a straightforward intuitive meaning to the practitioner. This will maximise chance of obtaining a reliable matrix. This construction is illustrated by a numerical example.

Systemic risk (SR) has been shown to play an important role in explaining the financial turmoils in the last several decades and understanding this source of risk has been a particular interest amongst academics, practitioners and regulators. The precise mathematical formulation of SR is still scrutinised, but the main purpose is to evaluate the financial distress of a system as a result of the failure of one component of the financial system in question. Many of the mathematical definitions of SR are based on evaluating expectations in extreme regions and therefore, Extreme Value Theory (EVT) represents the key ingredient in producing valuable estimates of SR and even its decomposition per individual components of the entire system. Without doubt, the prescribed dependence model amongst the system components has a major impact over our asymptotic approximations. Thus, this paper considers various well-known dependence models in the EVT literature that allow us to generate SR estimates. Our findings reveal that SR has a significant impact under asymptotic dependence, while weak tail dependence, known as asymptotic independence, produces an insignificant loss over the regulatory capital.