On some aspects of coherent risk measures and their applications

Le sujet principal de cette thèse porte sur les mesures de risque. L'objectif général est d'investiguer certains aspects des mesures de risque dans les applications financières. Le cadre théorique de ce travail est celui des mesures cohérentes de risque telle que définie dans Artzner et al (1999). Mais ce n'est pas la seule classe de mesure du risque que nous étudions. Par exemple, nous étudions aussi quelques aspects des "statistiques naturelles de risque" (en anglais natural risk statistics) Kou et al (2006) et des mesures convexes du risque Follmer and Schied(2002). Les contributions principales de cette thèse peuvent être regroupées selon trois axes: allocation de capital, évaluation des risques et capital requis et solvabilité. Dans le chapitre 2 nous caractérisons les mesures de risque avec la propriété de Lebesgue sur l'ensemble des processus bornés càdlàg (continu à droite, limité à gauche). Cette caractérisation nous permet de présenter deux applications dans l'évaluation des risques et l'allocation de capital. Dans le chapitre 3, nous étendons la notion de statistiques naturelles de risque à l'espace des suites infinies. Cette généralisation nous permet de construire de façon cohérente des mesures de risque pour des bases de données de n'importe quelle taille. Dans le chapitre 4, nous discutons le concept de "bonnes affaires" (en anglais Good Deals), pour notamment caractériser les situations du marché où ces positions pathologiques sont présentes. Finalement, dans le chapitre 5, nous essayons de relier les trois chapitres en étendant la définition de "bonnes affaires" dans un cadre plus large qui comprendrait les mesures de risque analysées dans les chapitres 2 et 3.

On the design of customized risk measures in insurance, the problem of capital allocation and the theory of fluctuations for Lévy processes

Dans cette thèse, nous étudions quelques problèmes fondamentaux en mathématiques financières et actuarielles, ainsi que leurs applications. Cette thèse est constituée de trois contributions portant principalement sur la théorie de la mesure de risques, le problème de l’allocation du capital et la théorie des fluctuations. Dans le chapitre 2, nous construisons de nouvelles mesures de risque cohérentes et étudions l’allocation de capital dans le cadre de la théorie des risques collectifs. Pour ce faire, nous introduisons la famille des "mesures de risque entropique cumulatifs" (Cumulative Entropic Risk Measures). Le chapitre 3 étudie le problème du portefeuille optimal pour le Entropic Value at Risk dans le cas où les rendements sont modélisés par un processus de diffusion à sauts (Jump-Diffusion). Dans le chapitre 4, nous généralisons la notion de "statistiques naturelles de risque" (natural risk statistics) au cadre multivarié. Cette extension non-triviale produit des mesures de risque multivariées construites à partir des données financiéres et de données d’assurance. Le chapitre 5 introduit les concepts de "drawdown" et de la "vitesse d’épuisement" (speed of depletion) dans la théorie de la ruine. Nous étudions ces concepts pour des modeles de risque décrits par une famille de processus de Lévy spectrallement négatifs.

Prevalence of malnutrition, obesity and nutritional risk of Australian paediatric inpatients: A national one-day snapshot

Aim Low prevalence rates of malnutrition at 2.5% to 4% have previously been reported in two tertiary paediatric Australian hospitals. The current study is the first to measure the prevalence of malnutrition, obesity and nutritional risk of paediatric inpatients in multiple hospitals throughout Australia. Methods Malnutrition, obesity and nutritional risk prevalence were investigated in 832 and 570 paediatric inpatients, respectively, in eight tertiary paediatric hospitals and eight regional hospitals across Australia on a single day. Malnutrition and obesity prevalence was determined using z-scores and body mass index (BMI) percentiles. High nutritional risk was determined as a Paediatric Yorkhill Malnutrition Score of 2 or more. Results The prevalence rates of malnourished, wasted, stunted, overweight and obese paediatric patients were 15%, 13.8%, 11.9%, 8.8% and 9.9%, respectively. Patients who identified as Aboriginal and Torres Strait Islander were more likely to have lower height-for-age z-scores (P < 0.01); however, BMI and weight-for-age z-scores were not significantly different. Children who were younger, from regional hospitals or with a primary diagnosis of cardiac disease or cystic fibrosis had significantly lower anthropometric z-scores (P = 0.05). Forty-four per cent of patients were identified as at high nutritional risk and requiring further nutritional assessment. Conclusions The prevalence of malnutrition and nutritional risk of Australian paediatric inpatients on a given day was much higher when compared with the healthy population. In contrast, the proportion of overweight and obese patients was less.

The role of fruit traits of bird-dispersed plants in invasiveness and weed risk assessment

Aim: Birds play a major role in the dispersal of seeds of many fleshy-fruited invasive plants. The fruits that birds choose to consume are influenced by fruit traits. However, little is known of how the traits of invasive plant fruits contribute to invasiveness or to their use by frugivores. We aim to gain a greater understanding of these relationships to improve invasive plant management. Location: South-east Queensland, Australia. Methods: We measure a variety of fruit morphology, pulp nutrient and phenology traits of a suite of bird-dispersed alien plants. Frugivore richness of these aliens was derived from the literature. Using regressions and multivariate methods, we investigate relationships between fruit traits, frugivore richness and invasiveness. Results: Plant invasiveness was negatively correlated to fruit size, and all highly invasive species had quite similar fruit morphology [smaller fruits, seeds of intermediate size and few (<10) seeds per fruit]. Lower pulp water was the only pulp nutrient trait associated with invasiveness. There were strong positive relationships between the diversity of bird frugivores and plant invasiveness, and in the diversity of bird frugivores in the study region and another part of the plants' alien range. Main conclusions: Our results suggest that weed risk assessments (WRA) and predictions of invasive success for bird-dispersed plants can be improved. Scoring criteria for WRA regarding fruit size would need to be system-specific, depending on the fruit-processing capabilities of local frugivores. Frugivore richness could be quantified in the plant's natural range, its invasive range elsewhere, or predictions made based on functionally similar fruits.

Physical activity, fitness, abdominal obesity, and cardiovascular risk factors in Finnish men and women : The National FINRISK 2002 Study

Physical inactivity, low cardiorespiratory fitness, and abdominal obesity are direct and mediating risk factors for cardiovascular disease (CVD). The results of recent studies suggest that individuals with higher levels of physical activity or cardiorespiratory fitness have lower CVD and all-cause mortality than those with lower activity or fitness levels regardless of their level of obesity. The interrelationships of physical activity, fitness, and abdominal obesity with cardiovascular risk factors have not been studied in detail. The aim of this study was to investigate the associations of different types of leisure time physical activity and aerobic fitness with cardiovascular risk factors in a large population of Finnish adults. In addition, a novel aerobic fitness test was implemented and the distribution of aerobic fitness was explored in men and women across age groups. The interrelationships of physical activity, aerobic fitness and abdominal obesity were examined in relation to cardiovascular risk factors. This study was part of the National FINRISK Study 2002, which monitors cardiovascular risk factors in a Finnish adult population. The sample comprised 13 437 men and women aged 25 to 74 years and was drawn from the Population Register as a stratified random sample according to 10-year age groups, gender and area. A separate physical activity study included 9179 subjects, of whom 5 980 participated (65%) in the study. At the study site, weight, height, waist and hip circumferences, and blood pressure were measured, a blood sample was drawn, and an aerobic fitness test was performed. The fitness test estimated maximal oxygen uptake (VO2max) and was based on a non-exercise method by using a heart rate monitor at rest. Waist-to-hip ratio (WHR) was calculated by dividing waist circumference with hip circumference and was used as a measure of abdominal obesity. Participants filled in a questionnaire on health behavior, a history of diseases, and current health status, and a detailed 12-month leisure time physical activity recall. Based on the recall data, relative energy expenditure was calculated using metabolic equivalents, and physical activity was divided into conditioning, non-conditioning, and commuting physical activity. Participants aged 45 to 74 years were later invited to take part in a 2-hour oral glucose tolerance test with fasting insulin and glucose measurements. Based on the oral glucose tolerance test, undiagnosed impaired glucose tolerance and type 2 diabetes were defined. The estimated aerobic fitness was lower among women and decreased with age. A higher estimated aerobic fitness and a lower WHR were independently associated with lower systolic and diastolic blood pressure, lower total cholesterol and triglyceride levels, and with higher high-density lipoprotein (HDL) cholesterol and HDL to total cholesterol ratio. The associations of the estimated aerobic fitness with diastolic blood pressure, triglycerides, and HDL to total cholesterol ratio were stronger in men with a higher WHR. High levels of conditioning and non-conditioning physical activity were associated with lower high-sensitivity C-reactive protein (CRP) levels. High levels of conditioning and overall physical activities were associated with lower insulin and glucose levels. The associations were stronger among women than men. A better self-rated physical fitness was associated with a higher estimated aerobic fitness, lower CRP levels, and lower insulin and glucose levels in men and women. In each WHR third, the risk of impaired glucose tolerance and type 2 diabetes was higher among physically inactive individuals who did not undertake at least 30 minutes of moderate-intensity physical activity on five days per week. These cross-sectional data show that higher levels of estimated aerobic fitness and regular leisure time physical activity are associated with a favorable cardiovascular risk factor profile and that these associations are present at all levels of abdominal obesity. Most of the associations followed a dose-response manner, suggesting that already low levels of physical activity or fitness are beneficial to health and that larger improvements in risk factor levels may be gained from higher activity and fitness levels. The present findings support the recommendation to engage regularly in leisure time physical activity, to pursue a high level of aerobic fitness, and to prevent abdominal obesity.

House value as an indicator of cumulative wealth is strongly related to morbidity and mortality risk in older people: a census-based cross-sectional and longitudinal study

Background: There has been relatively little research into health inequalities in older populations. This may be partly explained by the difficulty in identifying appropriate indicators of socio-economic status for older people. Ideally, indicators of socio-economic status to be used in studies of health inequalities in older populations should incorporate some measure of life-time socio-economic standing, and house value may fill this role. This study examined whether an indicator of accumulated wealth based on a combination of housing tenure and house value was a strong predictor of ill-health in older populations.
Methods: A total of 191 848 people aged =65 years and not living in communal establishments were identified from the 2001 Northern Ireland Census and followed for 5 years. Self-reported health and mortality risk by housing tenure/house value groupings were examined while controlling for a range of other demographic and socio-economic characteristics.
Results: Housing tenure/house value was highly correlated with other indicators of socio-economic status. Public-sector renters had worse self-reported health and higher mortality rates than owner occupiers but significant gradients were also found between those living in the highest-and lowest-valued owner-occupier properties. The relationship between housing tenure and value was unchanged by adjustment for indicators of social support and quality of the physical environment. Adjustment for limiting long-term illness and self-reported health at baseline narrowed but did not eliminate the health gains associated with living in more expensive housing.
Conclusions: House value of residence is an accessible and powerful indicator of accumulated wealth that is highly correlated with current health status and predictive of future mortality risk in older populations.

Religion and the risk of suicide: longitudinal study of over 1 million people

Background: Durkheim’s seminal historical study demonstrated that religious affiliation reduces suicide risk, but it is unclear whether this protective effect persists in modern, more secular societies.

Aims: To examine suicide risk according to Christian religious affiliation and by inference to examine underlying mechanisms for suicide risk. If church attendance is important, risk should be lowest for Roman Catholics and highest for those with no religion; if religiosity is important, then ‘conservative’ Christians should fare best.

Method: A 9-year study followed 1 106 104 people aged 16–74 years at the 2001 UK census, using Cox proportional hazards models adjusted for census-based cohort attributes.

Results: In fully adjusted models analysing 1119 cases of suicide, Roman Catholics, Protestants and those professing no religion recorded similar risks. The risk associated with conservative Christians was lower than that for Catholics (HR = 0.71, 95% CI 0.52–0.97).

Conclusions: The relationship between religious affiliation and suicide established by Durkheim may not pertain in societies where suicide rates are highest at younger ages. Risks are similar for those with and without a religious affiliation, and Catholics (who traditionally are characterised by higher levels of church attendance) do not demonstrate lower risk of suicide. However, religious affiliation is a poor measure of religiosity, except for a small group of conservative Christians, although their lower risk of suicide may be attributable to factors such as lower risk behaviour and alcohol consumption.

Properties of a risk measure derived from ruin theory

This paper studies a risk measure inherited from ruin theory and investigates some of its properties. Specifically, we consider a value-at-risk (VaR)-type risk measure defined as the smallest initial capital needed to ensure that the ultimate ruin probability is less than a given level. This VaR-type risk measure turns out to be equivalent to the VaR of the maximal deficit of the ruin process in infinite time. A related Tail-VaR-type risk measure is also discussed.

Linking community variables to parenting behaviours and youth risk behaviours

The puq)ose of this thesis is to test a model Hnking community disadvantage and urbanicity factors to parenting variables (i.e., monitoring, warmth, and knowledge) and to youth risk behavior (i.e., substance use and delinquency), measured both concurrently and one year after the assessment of parenting variables. The model builds on the work of Fletcher, Steinberg, and Williams-Wheeler (2004) but a) includes a more comprehensive measure of SES than that conceptualized by Fletcher et al.; b) considers whether the role of community disadvantage is indirectly as well as directly linked to youth risk behavior, by way of its association with parenting variables; c) considers whether level of community urbanicity plays a direct role in predicting both parenting variables and risk behaviors, or whether its influence on risk behaviours is primarily indirect through parenting variables. Both community disadvantage and urbanicity had virtually no relation to parenting and risk behaviour variables. Results found for relations of parenting variables and risk behaviour were similar to Fletcher et al. Although urban youth are typically perceived as being more at risk for substance use and delinquency, no evidence was found for a distinction between urban and rural youth within this sample. Targeting risk behaviour prevention/reduction programs toward only urban youth, therefore, is not supported by these findings.

Overall and income specific effect on prevalence of overweight and obesity of 20% sugar sweetened drink tax in UK: econometric and comparative risk assessment modelling study

Objective To model the overall and income specific effect of a 20% tax on sugar sweetened drinks on the prevalence of overweight and obesity in the UK. Design Econometric and comparative risk assessment modelling study. Setting United Kingdom. Population Adults aged 16 and over. Intervention A 20% tax on sugar sweetened drinks. Main outcome measures The primary outcomes were the overall and income specific changes in the number and percentage of overweight (body mass index ≥25) and obese (≥30) adults in the UK following the implementation of the tax. Secondary outcomes were the effect by age group (16-29, 30-49, and ≥50 years) and by UK constituent country. The revenue generated from the tax and the income specific changes in weekly expenditure on drinks were also estimated. Results A 20% tax on sugar sweetened drinks was estimated to reduce the number of obese adults in the UK by 1.3% (95% credible interval 0.8% to 1.7%) or 180 000 (110 000 to 247 000) people and the number who are overweight by 0.9% (0.6% to 1.1%) or 285 000 (201 000 to 364 000) people. The predicted reductions in prevalence of obesity for income thirds 1 (lowest income), 2, and 3 (highest income) were 1.3% (0.3% to 2.0%), 0.9% (0.1% to 1.6%), and 2.1% (1.3% to 2.9%). The effect on obesity declined with age. Predicted annual revenue was £276m (£272m to £279m), with estimated increases in total expenditure on drinks for income thirds 1, 2, and 3 of 2.1% (1.4% to 3.0%), 1.7% (1.2% to 2.2%), and 0.8% (0.4% to 1.2%). Conclusions A 20% tax on sugar sweetened drinks would lead to a reduction in the prevalence of obesity in the UK of 1.3% (around 180 000 people). The greatest effects may occur in young people, with no significant differences between income groups. Both effects warrant further exploration. Taxation of sugar sweetened drinks is a promising population measure to target population obesity, particularly among younger adults.

Evidence on the relationship between incentives and exogenous risk

Theoretical models on moral hazard provide competing predictions on the incentive-risk relationship. These predictions are derived under the assumptions of homogeneous agents and exogenous risk. However, the existing empirical evidence does not account for risk-aversion heterogeneity and risk endogeneity. This paper uses a well-built database on tenancy contracts to address these issues. Detailed information on cropping activities is used to measure the exogenous risk. Risk-aversion heterogeneity and other self-selection problems are addressed through a portfolio schedule and a subsample of farmers who simultaneously own and sharecrop different farms. This controlled exercise finds a direct relation between incentives and exogenous risk.

Risky business: social media metrics and political risk analysis

A quantificação do risco país – e do risco político em particular – levanta várias dificuldades às empresas, instituições, e investidores. Como os indicadores econômicos são atualizados com muito menos freqüência do que o Facebook, compreender, e mais precisamente, medir – o que está ocorrendo no terreno em tempo real pode constituir um desafio para os analistas de risco político. No entanto, com a crescente disponibilidade de “big data” de ferramentas sociais como o Twitter, agora é o momento oportuno para examinar os tipos de métricas das ferramentas sociais que estão disponíveis e as limitações da sua aplicação para a análise de risco país, especialmente durante episódios de violência política. Utilizando o método qualitativo de pesquisa bibliográfica, este estudo identifica a paisagem atual de dados disponíveis a partir do Twitter, analisa os métodos atuais e potenciais de análise, e discute a sua possível aplicação no campo da análise de risco político. Depois de uma revisão completa do campo até hoje, e tendo em conta os avanços tecnológicos esperados a curto e médio prazo, este estudo conclui que, apesar de obstáculos como o custo de armazenamento de informação, as limitações da análise em tempo real, e o potencial para a manipulação de dados, os benefícios potenciais da aplicação de métricas de ferramentas sociais para o campo da análise de risco político, particularmente para os modelos qualitativos-estruturados e quantitativos, claramente superam os desafios.

The relationship between calcium and fluoride intake, pregnancy and lactation and the risk of height loss in white women

This study was designed to investigate the effect of calcium and fluoride intake, and parity and lactation on the risk of spinal osteoporosis. Height loss was used as a surrogate measure for spinal fractures by taking advantage of documented changes in height found during the 25-year follow-up of the Charleston Heart Study cohort. Women who had lost 2-4" in height or who had no change in height during the follow-up period were defined as case and comparison subjects respectively. Calcium intake when the subjects were "about 25" and in the recent past, average intake of fluoride over 25 years, and parity and history of breastfeeding were ascertained by questionnaire from 54 case and 77 comparison subjects. Low calcium intake in the past decreased the risk of height loss (age-adjusted OR = 0.3, 95%CI: 0.1-0.96) although several potentially important confounding variables could not be adjusted for. There was no association between risk of height loss and present calcium intake (OR = 0.8, 95%CI: 0.3-2.6 for low versus high intake) after adjustment for past calcium intake. High fluoride intake decreased the risk of height loss (adjusted OR = 0.4, 95%CI: 0.1-1.2). The effect of fluoride or calcium intake in the present was modified by the level of the other nutrient. Compared to a low intake of both calcium and fluoride, a high intake of one increased the risk of height loss (crude OR = 3.3 for high fluoride/low calcium, crude OR = 6.0 for high calcium/low fluoride) although a high intake of both was slightly protective (crude OR = 0.7). It is estimated that a "high" nutrient intake in this population was greater than 850mg/day for calcium and 2mg/day for fluoride. After adjustment for age, increasing parity decreased the risk of height loss in women who had never breastfed (OR = 0.2, 95%CI: 0.01-1.7 for 4 or more children). Women who had breastfed were also at lower risk of height loss than nulliparous women (OR = 0.3, 95%CI: 0.1-1.2 for 4 or more children) although at any level of parity, breastfeeding women had a greater risk of height loss than did non-breastfeeding women. ^

Association between length of stay in the U.S. and diabetes risk factors among Chinese Americans in Houston, Texas in 2004-2005

Studies have suggested that acculturation is related to diabetes prevalence and risk factors among immigrant groups in the United States (U.S.), however scant data are available to investigate this relationship among Asian Americans and Asian American subgroups. The objective of this cross-sectional study was to examine the association between length of stay in the U.S. and type 2 diabetes prevalence and its risk factors among Chinese Americans in Houston, Texas. Data were obtained from the 2004-2005 Asian-American Health Needs Assessment in Houston, Texas (N=409 Chinese Americans) for secondary analysis in this study. Diabetes prevalence and risk factors (overweight/obesity and access to medical care) were based on self-report. Descriptive statistics summarized demographic characteristics, diabetes prevalence, and reasons for not seeing a doctor. Logistic regression, using an incremental modeling approach, was used to measure the association between length of stay and diabetes prevalence and related risk factors, while adjusting for the potential confounding factors of age, gender, education level, and income level. Although the prevalence of type 2 diabetes was highest among those living in the U.S. for more than 20 years, there was no significant association between length of stay in the U.S. and diabetes prevalence among these Chinese Americans after adjustment for confounding factors. No association was found between length of stay in the U.S. and overweight/obese status among this population either, after adjusting for confounding factors, too. On the other hand, a longer length of stay was significantly associated with increased health insurance coverage in both unadjusted and adjusted models. The findings of this study suggest that length of stay in the U.S. alone may not be an indicator for diabetes risk among Chinese Americans. Future research should consider alternative models to measure acculturation (e.g., models that reflect acculturation as a multi-dimensional, not uni-dimensional process), which may more accurately depict its effect on diabetes prevalence and related risk factors.^

Troponin I and cardiovascular risk prediction in the general population: the BiomarCaRE consortium

AIMS: Our aims were to evaluate the distribution of troponin I concentrations in population cohorts across Europe, to characterize the association with cardiovascular outcomes, to determine the predictive value beyond the variables used in the ESC SCORE, to test a potentially clinically relevant cut-off value, and to evaluate the improved eligibility for statin therapy based on elevated troponin I concentrations retrospectively.

METHODS AND RESULTS: Based on the Biomarkers for Cardiovascular Risk Assessment in Europe (BiomarCaRE) project, we analysed individual level data from 10 prospective population-based studies including 74 738 participants. We investigated the value of adding troponin I levels to conventional risk factors for prediction of cardiovascular disease by calculating measures of discrimination (C-index) and net reclassification improvement (NRI). We further tested the clinical implication of statin therapy based on troponin concentration in 12 956 individuals free of cardiovascular disease in the JUPITER study. Troponin I remained an independent predictor with a hazard ratio of 1.37 for cardiovascular mortality, 1.23 for cardiovascular disease, and 1.24 for total mortality. The addition of troponin I information to a prognostic model for cardiovascular death constructed of ESC SCORE variables increased the C-index discrimination measure by 0.007 and yielded an NRI of 0.048, whereas the addition to prognostic models for cardiovascular disease and total mortality led to lesser C-index discrimination and NRI increment. In individuals above 6 ng/L of troponin I, a concentration near the upper quintile in BiomarCaRE (5.9 ng/L) and JUPITER (5.8 ng/L), rosuvastatin therapy resulted in higher absolute risk reduction compared with individuals <6 ng/L of troponin I, whereas the relative risk reduction was similar.

CONCLUSION: In individuals free of cardiovascular disease, the addition of troponin I to variables of established risk score improves prediction of cardiovascular death and cardiovascular disease.