Poisson Incorporated Credibility Regression Modelling of Systematic Mortality Risk for Populations with Finite Data

Abstract

This study considered the modeling of systematic mortality risk for populations with finite data using the Poisson incorporated Credibility regression model. For novelty, we have included the credibility regression approach to modelling mortality by assuming the number of annual deaths follow a Poisson distribution. Our model shows improvement in precision levels when estimating mortality risk compared to classical models used in European countries. We have illustrated that our model works optimally when using Kenyan mortality data, comparing male and female lives under the different strategies, thus making better predictions than the classical Lee–Carter (LC) and Cairns–Blake–Dowd (CBD) models. The mean absolute forecast error (MAFE), mean absolute percentage forecast error (MAPFE), root mean square error (RMSE), and root mean square forecast error (RMSFE) under the incorporated credibility regression model are much lower than the values obtained without incorporation of the Buhlmann credibility approach. The findings of this research will help insurance companies, pension firms, and government agencies in sub-Saharan countries model and forecast systematic mortality risks accurately. Finally, the results are essential in actuarial modelling and pricing, thus making life assurance products affordable for most people in low-income African countries.

Quantitative Representation of Disturbance Waveform for Microgrid Connected PCC Voltages Using Improved Atomic Decomposition

“…The atoms in the dictionary are usually obtained by scaling, transforming, and modulating some special functions. One of the common methods is to use Gabor as the mother function to form the Gabor atoms, as shown in Equation (2).…”

“…If the waveform is stored and transmitted in the form of sampling data, the dimension is huge and hard to deal with. If the data are modeled properly and only the modeling parameters are stored and transmitted, the data dimension will be reduced greatly [2][3][4].…”

Labor Force Participation Rate and Expected Length of Retirement 2001-2047: A Case Study in Malaysia

“…CBD model with a cohort effect was found to provide the greatest fit for males in England and Wales [36], whereas the quadratic CBD model showed the best fit to mortality data in other studies [37]. However, other research indicated that variants of Lee-Carter model better suit their data [31], [38], [39]. For simplicity of this research, the standard Lee-Carter model and CBD model were utilized to compare the LFPR forecast for higher ages.…”

“…Several research suggested tweaks to the Lee-Carter model that would make it more effective at modeling and forecasting rates. Some examples of these adjustments are using a Bayesian method [30] incorporating randomness or an error term into the model [30], [31], or employing a state-space model to get around the biodemographic constraint and using resampling method to improve forecasting accuracy [32]. Moreover, Lee-Carter model has been contrasted with other models, including the neural networks [33], autoregressive integrated moving average (ARIMA) model [34], and modified Lee-Carter model with bias-corrected estimators [35].…”

Deep Learning Incorporated Bühlmann Credibility in the Modified Lee–Carter Mortality Model

“…Today, several extensions and applications have been made, making actuarial science literature rich in terms of mortality modeling techniques. Also, the freeware statistical R package has included many packages, namely, "StMoMo," "demography," "acturyr," and "gnm," thus helping in forecasting the rates of future mortality and at the same time ftting a model of time series especially to the predicted rates of the mortality index, see [2,4,[13][14][15][16][17]. Deep learning mortality modeling has been conducted in [18], thus making it one of novel methodologies to deal with data paucity in developing countries.…”