Economics - Research Publications
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ItemOptimal strategies for the decumulation of retirement savings under differing appetites for liquidity and investment risks(SPRINGER INT PUBL AG, 2024-01-01)A retiree’s appetite for risk is a common input into the lifetime utility models that are traditionally used to find optimal strategies for the decumulation of retirement savings. In this work, we consider a retiree with potentially differing appetites for the key financial risks of decumulation: liquidity risk and investment risk. We set out to determine whether these differing risk appetites have a significant impact on the retiree’s optimal choice of decumulation strategy. To do so, we design and implement a framework which selects the optimal decumulation strategy from a general set of admissible strategies in line with a retiree’s goals, and under differing appetites for the key risks of decumulation. Overall, we find significant evidence to suggest that a retiree’s differing appetites for different decumulation risks will impact their optimal choice of strategy at retirement. Through an illustrative example calibrated to the Australian context, we find results which are consistent with actual behaviours in this jurisdiction (in particular, a shallow market for annuities), which lends support to our framework and may provide some new insight into the so-called annuity puzzle.
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ItemStable dividends under linear-quadratic optimisation(ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD, 2023-09-02)The optimisation criterion for dividends from a risky business is most often formalised in terms of the expected present value of future dividends. That criterion disregards a potential, explicit demand for the stability of dividends. In particular, within actuarial risk theory, the maximisation of future dividends has been studied as the so-called de Finetti problem. However, there the optimal strategies typically become so-called barrier strategies. These are far from stable, and suboptimal affine dividend strategies have recently received attention. In contrast, in the class of linear-quadratic problems, the demand for stability is explicitly stressed. These have often been studied in diffusion models different from the actuarial risk models. We bridge the gap between these thinking patterns by deriving optimal affine dividend strategies under a linear-quadratic criterion for an additive process. We characterise the value function by the Hamilton-Jacobi-Bellman equation, solve it, and compare the objective and the optimal controls to the classical objective of maximising the expected present value of future dividends. Thereby we provide a framework within which stability of dividends from a risky business, e.g. in classical risk theory, is explicitly demanded and obtained.
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ItemOptimal reinsurance design under solvency constraints(Informa UK Limited, 2024-01-01)We consider the optimal risk transfer from an insurance company to a reinsurer. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some crucial distinctions. In particular, the insurance company's surplus is here (as is routinely the case) approximated by a Brownian motion, as opposed to the geometric Brownian motion used to model assets in finance. Furthermore, risk exposure is dialled ‘down’ via reinsurance, rather than ‘up’ via risky investments. This leads to interesting qualitative differences in the optimal designs. In this paper, using the martingale method, we derive the optimal design as a function of proportional, non-cheap reinsurance design that maximises the quadratic utility of the terminal value of the insurance surplus. We also consider several realistic constraints on the terminal value: a strict lower boundary, the probability (Value at Risk) constraint, and the expected shortfall (conditional Value at Risk) constraints under the (Formula presented.) and (Formula presented.) measures, respectively. In all cases, the optimal reinsurance designs boil down to a combination of proportional protection and option-like protection (stop-loss) of the residual proportion with various deductibles. Proportions and deductibles are set such that the initial capital is fully allocated. Comparison of the optimal designs with the optimal portfolios in finance is particularly interesting. Results are illustrated.
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ItemMachine Learning with High-Cardinality Categorical Features in Actuarial Applications(CAMBRIDGE UNIV PRESS, 2024-05-11)High-cardinality categorical features are pervasive in actuarial data (e.g., occupation in commercial property insurance). Standard categorical encoding methods like one-hot encoding are inadequate in these settings. In this work, we present a novel Generalised Linear Mixed Model Neural Network (GLMMNet) approach to the modelling of high-cardinality categorical features. The GLMMNet integrates a generalised linear mixed model in a deep learning framework, offering the predictive power of neural networks and the transparency of random effects estimates, the latter of which cannot be obtained from the entity embedding models. Further, its flexibility to deal with any distribution in the exponential dispersion (ED) family makes it widely applicable to many actuarial contexts and beyond. In order to facilitate the application of GLMMNet to large datasets, we use variational inference to estimate its parameters - both traditional mean field and versions utilising textual information underlying the high-cardinality categorical features. We illustrate and compare the GLMMNet against existing approaches in a range of simulation experiments as well as in a real-life insurance case study. A notable feature for both our simulation experiment and the real-life case study is a comparatively low signal-to-noise ratio, which is a feature common in actuarial applications. We find that the GLMMNet often outperforms or at least performs comparably with an entity-embedded neural network in these settings, while providing the additional benefit of transparency, which is particularly valuable in practical applications. Importantly, while our model was motivated by actuarial applications, it can have wider applicability. The GLMMNet would suit any applications that involve high-cardinality categorical variables and where the response cannot be sufficiently modelled by a Gaussian distribution, especially where the inherent noisiness of the data is relatively high.
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ItemStatistical analyses of ordinal outcomes in randomised controlled trials: a scoping review(BMC, 2024-04-06)BACKGROUND: Randomised controlled trials (RCTs) aim to estimate the causal effect of one or more interventions relative to a control. One type of outcome that can be of interest in an RCT is an ordinal outcome, which is useful to answer clinical questions regarding complex and evolving patient states. The target parameter of interest for an ordinal outcome depends on the research question and the assumptions the analyst is willing to make. This review aimed to provide an overview of how ordinal outcomes have been used and analysed in RCTs. METHODS: The review included RCTs with an ordinal primary or secondary outcome published between 2017 and 2022 in four highly ranked medical journals (the British Medical Journal, New England Journal of Medicine, The Lancet, and the Journal of the American Medical Association) identified through PubMed. Details regarding the study setting, design, the target parameter, and statistical methods used to analyse the ordinal outcome were extracted. RESULTS: The search identified 309 studies, of which 144 were eligible for inclusion. The most used target parameter was an odds ratio, reported in 78 (54%) studies. The ordinal outcome was dichotomised for analysis in 47 ( 33 % ) studies, and the most common statistical model used to analyse the ordinal outcome on the full ordinal scale was the proportional odds model (64 [ 44 % ] studies). Notably, 86 (60%) studies did not explicitly check or describe the robustness of the assumptions for the statistical method(s) used. CONCLUSIONS: The results of this review indicate that in RCTs that use an ordinal outcome, there is variation in the target parameter and the analytical approaches used, with many dichotomising the ordinal outcome. Few studies provided assurance regarding the appropriateness of the assumptions and methods used to analyse the ordinal outcome. More guidance is needed to improve the transparent reporting of the analysis of ordinal outcomes in future trials.
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ItemOn the impact of outliers in loss reserving(SPRINGER HEIDELBERG, 2024-04)Abstract The sensitivity of loss reserving techniques to outliers in the data or deviations from model assumptions is a well known challenge. It has been shown that the popular chain-ladder reserving approach is at significant risk to such aberrant observations in that reserve estimates can be significantly shifted in the presence of even one outlier. As a consequence the chain-ladder reserving technique is non-robust. In this paper we investigate the sensitivity of reserves and mean squared errors of prediction under Mack’s Model (ASTIN Bull 23(2):213–225, 1993). This is done through the derivation of impact functions which are calculated by taking the first derivative of the relevant statistic of interest with respect to an observation. We also provide and discuss the impact functions for quantiles when total reserves are assumed to be lognormally distributed. Additionally, comparisons are made between the impact functions for individual accident year reserves under Mack’s Model and the Bornhuetter–Ferguson methodology. It is shown that the impact of incremental claims on these statistics of interest varies widely throughout a loss triangle and is heavily dependent on other cells in the triangle. Results are illustrated using data from a Belgian non-life insurer.
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ItemDetection and treatment of outliers for multivariate robust loss reserving(CAMBRIDGE UNIV PRESS, 2024-03)Abstract Traditional techniques for calculating outstanding claim liabilities such as the chain-ladder are notoriously at risk of being distorted by outliers in past claims data. Unfortunately, the literature in robust methods of reserving is scant, with notable exceptions such as Verdonck & Debruyne (2011, Insurance: Mathematics and Economics, 48, 85–98) and Verdonck & Van Wouwe (2011, Insurance: Mathematics and Economics,49, 188–193). In this paper, we put forward two alternative robust bivariate chain-ladder techniques to extend the approach of Verdonck & Van Wouwe (2011, Insurance: Mathematics and Economics,49, 188–193). The first technique is based on Adjusted Outlyingness (Hubert & Van der Veeken, 2008. Journal of Chemometrics,22, 235–246) and explicitly incorporates skewness into the analysis while providing a unique measure of outlyingness for each observation. The second technique is based on bagdistance (Hubert et al., 2016. Statistics: Methodology, 1–23) which is derived from the bagplot; however; it is able to provide a unique measure of outlyingness and a means to adjust outlying observations based on this measure. Furthermore, we extend our robust bivariate chain-ladder approach to an N-dimensional framework. The implementation of the methods, especially beyond bivariate, is not trivial. This is illustrated on a trivariate data set from Australian general insurers and results under the different outlier detection and treatment mechanisms are compared.
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ItemPosterior Manifolds over Prior Parameter Regions: Beyond Pointwise Sensitivity Assessments for Posterior Statistics from MCMC Inference(De Gruyter, 2023)Increases in the use of Bayesian inference in applied analysis, the complexity of estimated models, and the popularity of efficient Markov chain Monte Carlo (MCMC) inference under conjugate priors have led to more scrutiny regarding the specification of the parameters in prior distributions. Impact of prior parameter assumptions on posterior statistics is commonly investigated in terms of local or pointwise assessments, in the form of derivatives or more often multiple evaluations under a set of alternative prior parameter specifications. This paper expands upon these localized strategies and introduces a new approach based on the graph of posterior statistics over prior parameter regions (sensitivity manifolds) that offers additional measures and graphical assessments of prior parameter dependence. Estimation is based on multiple point evaluations with Gaussian processes, with efficient selection of evaluation points via active learning, and is further complemented with derivative information. The application introduces a strategy to assess prior parameter dependence in a multivariate demand model with a high dimensional prior parameter space, where complex prior-posterior dependence arises from model parameter constraints. The new measures uncover a considerable prior dependence beyond parameters suggested by theory, and reveal novel interactions between the prior parameters and the elasticities.
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ItemNo Preview AvailableNon-linear associations between HPA axis activity during infancy and mental health difficulties during early childhood among children in rural Pakistan(CAMBRIDGE UNIV PRESS, 2023-10)Hypothalamic pituitary adrenal (HPA) axis activity may be a mechanism linking early adversity to child mental health difficulties. However, there is a dearth of longitudinal evidence for the association between HPA axis activity and mental health among children in low-resource contexts. The goal of this study is to examine linear and curvilinear associations between HPA axis activity during infancy and mental health difficulties in early childhood among children in rural Pakistan. Participants included 104 children (46% male) from the Bachpan study, a longitudinal cohort embedded within a maternal depression trial in Pakistan. We examined the associations between hair-derived cortisol and dehydroepiandosterone (DHEA) at 12 months old and mental health difficulties, measured with the Strengths and Difficulties Questionnaire (SDQ), at 36 months old. There was a significant quadratic association between hair cortisol and SDQ scores, with results showing a U-shaped relationship (i.e., having relatively high or low cortisol predicted increased mental health difficulties). DHEA showed a quadratic association with SDQ scores with an inverted U-shaped relationship (i.e., high and low DHEA was associated with decreased mental health difficulties). Results provide evidence of longitudinal and curvilinear effects of cortisol and DHEA during infancy on mental health difficulties in early childhood.
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ItemNo Preview AvailableEconomic conditions and health: Local effects, national effect and local area heterogeneity(Elsevier BV, 2023-10-01)