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Modelling mortality co-movements for multiple populations has significant implications for mortality/longevity risk management. This paper assumes that multiple populations are heterogeneous sub-populations randomly drawn from a hypothetical super-population. Those heterogeneous sub-populations may exhibit various patterns of mortality dynamics across different age groups. We propose a hierarchical structure of these age patterns to ensure the model stability and use a Vector Error Correction Model (VECM) to fit the co-movements over time. Especially, a structural analysis based on the VECM is implemented to investigate potential interdependence among mortality dynamics of the examined populations. An efficient Bayesian Markov Chain Monte-Carlo method is also developed to estimate the unknown parameters to address the computational complexity. Our empirical application to the mortality data collected for the Group of Seven nations demonstrates the efficacy of our approach.
Modeling and forecasting of mortality rates are closely related to a wide range of actuarial practices, such as the designing of pension schemes. To improve the forecasting accuracy, age coherence is incorporated in many recent mortality models, which suggests that the long-term forecasts will not diverge infinitely among age groups. Despite their usefulness, misspecification is likely to occur for individual mortality models when applied in empirical studies. The reliableness and accuracy of forecast rates are therefore negatively affected. In this study, an ensemble averaging or model averaging (MA) approach is proposed, which adopts age-specific weights and asymptotically achieves age coherence in mortality forecasting. The ensemble space contains both newly developed age-coherent and classic age-incoherent models to achieve the diversity. To realize the asymptotic age coherence, consider parameter errors, and avoid overfitting, the proposed method minimizes the variance of out-of-sample forecasting errors, with a uniquely designed coherent penalty and smoothness penalty. Our empirical data set include ten European countries with mortality rates of 0–100 age groups and spanning 1950–2016. The outstanding performance of MA is presented using the empirical sample for mortality forecasting. This finding robustly holds in a range of sensitivity analyses. A case study based on the Italian population is finally conducted to demonstrate the improved forecasting efficiency of MA and the validity of the proposed estimation of weights, as well as its usefulness in actuarial applications such as the annuity pricing.
Novel navigation applications provide a driving behavior score for each finished trip to promote safe driving, which is mainly based on experts’ domain knowledge. In this paper, with automobile insurance claims data and associated telematics car driving data, we propose a supervised driving risk scoring neural network model. This one-dimensional convolutional neural network takes time series of individual car driving trips as input and returns a risk score in the unit range of (0,1). By incorporating credibility average risk score of each driver, the classical Poisson generalized linear model for automobile insurance claims frequency prediction can be improved significantly. Hence, compared with non-telematics-based insurers, telematics-based insurers can discover more heterogeneity in their portfolio and attract safer drivers with premiums discounts.
Major depressive disorder (MDD) is a clinically and biologically heterogeneous syndrome. Identifying discrete subtypes of illness with distinguishing neurobiological substrates and clinical features is a promising strategy for guiding personalised therapeutics.
This study aimed to identify depression subtypes with correlated patterns of functional network connectivity and clinical symptoms by clustering patients according to a weighted linear combination of both features in a relatively large, medication-naïve depression sample.
We recruited 115 medication-naïve adults with MDD and 129 matched healthy controls, and evaluated all participants with magnetic resonance imaging. We used regularised canonical correlation analysis to identify component mapping relationships between functional network connectivity and symptom profiles, and K-means clustering was used to define distinct subtypes of patients.
Two subtypes of MDD were identified: insomnia-dominated subtype 1 and anhedonia-dominated subtype 2. Subtype 1 was characterised by abnormal hyperconnectivity within the ventral attention network and sleep maintenance insomnia. Subtype 2 was characterised by abnormal hypoconnectivity in the subcortical and dorsal attention networks, and prominent anhedonia symptoms.
Our study identified two distinct subtypes of patients with specific neurobiological and clinical symptom profiles. These findings advance understanding of the biological and clinical heterogeneity of MDD, offering a pathway for defining categorical subtypes of illness via consideration of both biological and clinical features.
This paper investigates a high-dimensional vector-autoregressive (VAR) model in mortality modeling and forecasting. We propose an extension of the sparse VAR (SVAR) model fitted on the log-mortality improvements, which we name “spatially penalized smoothed VAR” (SSVAR). By adaptively penalizing the coefficients based on the distances between ages, SSVAR not only allows a flexible data-driven sparsity structure of the coefficient matrix but simultaneously ensures interpretable coefficients including cohort effects. Moreover, by incorporating the smoothness penalties, divergence in forecast mortality rates of neighboring ages is largely reduced, compared with the existing SVAR model. A novel estimation approach that uses the accelerated proximal gradient algorithm is proposed to solve SSVAR efficiently. Similarly, we propose estimating the precision matrix of the residuals using a spatially penalized graphical Lasso to further study the dependency structure of the residuals. Using the UK and France population data, we demonstrate that the SSVAR model consistently outperforms the famous Lee–Carter, Hyndman–Ullah, and two VAR-type models in forecasting accuracy. Finally, we discuss the extension of the SSVAR model to multi-population mortality forecasting with an illustrative example that demonstrates its superiority in forecasting over existing approaches.
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