An actuarial approach to assessing personal injury compensations in Singapore: Theory and practice

In Singapore personal injury litigations, successful claimants usually receive their compensations as a lump sum. The main advantage of a lump sum payment is that the proceedings can be concluded with a 'clean break' between the parties. The lump sum is a result of discounting the future pecuniary values into a single present-day amount, considering the time value of money and the claimant's mortality. Conventionally, lump sum awards are determined by making reference to a spread of amounts in comparable cases. However, a fairer method would be one that involves input from not only lawyers but also other experts including economists and actuaries. This study, which is carried out by an inter-professional working group, provides a set of actuarially computed tables for use in personal injury settlements in Singapore. The calculations involve a consideration of recent advancements in stochastic mortality modeling and an empirical study on the econometrics of real returns on risk-free assets in Singapore. We then present two recent personal injury cases in Singapore, aiming at helping the Singapore legal profession understand and use the economic principles with actuarial tables, and educating economists and actuaries the legal concerns and concepts in personal injury cases. © 2010 World Scientific Publishing Company.postprin

Using Actuarial Evidence in Singapore and Hong Kong: A Sequel to “Lai Wee Lian Revisited”

Following the English common law, successful claimants in personal injury and clinical negligence cases in Singapore and Hong Kong usually receive their compensations as a lump sum. The amount in respect of future expenses and loss of future earning is a result of discounting the future pecuniary values into a single present-day amount, considering inflation, the time value of money and the claimant’s mortality. Using actuarial tables based on projections of the mortality rate of the general population may be considered as an alternative method in converting the future loss of earnings and future expenses into a lump sum reflecting its present value. For this purpose, a set of actuarial tables are constructed in this article. Various options for determining the appropriate discount rate(s) are explored in the context of the statistical and economic data of Singapore and Hong Kong.published_or_final_versio

Assessing Personal Injury Liabilities in China from National to Provincial Level: An International Comparative Analysis

In a tort-based legal system, when a party is injured as a consequence of another party’s negligence, the party should be provided with sufficient compensation so that he or she may live as fulfilling a life as possible after the injury. The moral objective underlying this supposition is intuitively appealing. It is not surprising, therefore, that this jurisprudential notion is favourably regarded and widely applied in various common law and civilian jurisdictions, despite differences in tradition and culture. Nonetheless, although the two bodies of law share a similar objective in this respect, there are a number of differences in the substantive content of the law and the configuration of the rules. The present authors argue, and provide empirical evidence to support, that there are signs of convergence as both legal systems are in fact applying the same multiplicand-multiplier approach in assessing the quantum of damages. Case studies in mainland China (concerning civil law) and in the United Kingdom and Hong Kong (regarding common law) are adopted as the research methodology to explore the broader implications of this convergence

Immediate Risk for Cardiovascular Events in Hip Fracture Patients: A Population-Based Cohort Study

Background: Emerging evidence showed that bone metabolism and cardiovascular diseases (CVD) are closely related. We previously observed a potential immediate risk of cardiovascular mortality after hip fracture. However, whether there is an immediate risk of cardiovascular events after hip fracture is unclear. The aim of this study was to evaluate the risk for major adverse cardiovascular events (MACEs) between patients having experienced falls with and without hip fracture. / Methods: This retrospective population-based cohort study used data from a centralized electronic health record database managed by Hong Kong Hospital Authority. Patients having experienced falls with and without hip fracture were matched by propensity score (PS) at a 1:1 ratio. Adjusted associations between hip fracture and risk of MACEs were evaluated using competing risk regression after accounting for competing risk of death. / Results: Competing risk regression showed that hip fracture was associated with increased one-year risk of MACEs (hazard ratio [HR], 1.27; 95% CI, 1.21 to 1.33; p<0.001), with a 1-year cumulative incidence difference of 2.40% (1.94% to 2.87%). The HR was the highest in the first 90-day after hip fracture (HR of 1.32), and such an estimate was continuously reduced in 180-day, 270-day, and 1-year after hip fracture. / Conclusions: Hip fracture was associated with increased immediate risk of MACEs. This study suggested that a prompt evaluation of MACE among older adults aged 65 years and older who are diagnosed with hip fracture irrespectively of cardiovascular risk factors may be important, as early management may reduce subsequent risk of MACE

Sex-specific mortality forecasting for UK countries: a coherent approach

This paper introduces a gender specific model for the joint mortality projection of three countries (England and Wales combined, Scotland, and Northern Ireland) of the United Kingdom. The model, called 2-tier Augmented Common Factor model, extends the classical Lee and Carter [26] and Li and Lee [32] models, with a common time factor for the whole UK population, a sex specific period factor for males and females, and a specific time factor for each country within each gender. As death counts in each subpopulation are modelled directly, a Poisson framework is used. Our results show that the 2-tier ACF model improves the in-sample fitting compared to the use of independent LC models for each subpopulation or of independent Li and Lee models for each couple of genders within each country. Mortality projections also show that the 2-tier ACF model produces coherent forecasts for the two genders within each country and different countries within each gender, thus avoiding the divergence issues arising when independent projections are used. The 2-tier ACF is further extended to include a cohort term to take into account the faster improvements of the UK ‘golden generation’

Development and validation of sex-specific hip fracture prediction models using electronic health records: a retrospective, population-based cohort study

Background: Hip fracture is associated with immobility, morbidity, mortality, and high medical cost. Due to limited availability of dual-energy X-ray absorptiometry (DXA), hip fracture prediction models without using bone mineral density (BMD) data are essential. We aimed to develop and validate 10-year sex-specific hip fracture prediction models using electronic health records (EHR) without BMD. Methods: In this retrospective, population-based cohort study, anonymized medical records were retrieved from the Clinical Data Analysis and Reporting System for public healthcare service users in Hong Kong aged ≥60 years as of 31 December 2005. A total of 161,051 individuals (91,926 female; 69,125 male) with complete follow-up from 1 January 2006 till the study end date on 31 December 2015 were included in the derivation cohort. The sex-stratified derivation cohort was randomly divided into 80% training and 20% internal testing datasets. An independent validation cohort comprised 3046 community-dwelling participants aged ≥60 years as of 31 December 2005 from the Hong Kong Osteoporosis Study, a prospective cohort which recruited participants between 1995 and 2010. With 395 potential predictors (age, diagnosis, and drug prescription records from EHR), 10-year sex-specific hip fracture prediction models were developed using stepwise selection by logistic regression (LR) and four machine learning (ML) algorithms (gradient boosting machine, random forest, eXtreme gradient boosting, and single-layer neural networks) in the training cohort. Model performance was evaluated in both internal and independent validation cohorts. Findings: In female, the LR model had the highest AUC (0.815; 95% Confidence Interval [CI]: 0.805–0.825) and adequate calibration in internal validation. Reclassification metrics showed the LR model had better discrimination and classification performance than the ML algorithms. Similar performance was attained by the LR model in independent validation, with high AUC (0.841; 95% CI: 0.807–0.87) comparable to other ML algorithms. In internal validation for male, LR model had high AUC (0.818; 95% CI: 0.801–0.834) and it outperformed all ML models as indicated by reclassification metrics, with adequate calibration. In independent validation, the LR model had high AUC (0.898; 95% CI: 0.857–0.939) comparable to ML algorithms. Reclassification metrics demonstrated that LR model had the best discrimination performance. Interpretation: Even without using BMD data, the 10-year hip fracture prediction models developed by conventional LR had better discrimination performance than the models developed by ML algorithms. Upon further validation in independent cohorts, the LR models could be integrated into the routine clinical workflow, aiding the identification of people at high risk for DXA scan. Funding: Health and Medical Research Fund, Health Bureau, Hong Kong SAR Government (reference: 17181381)

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems