Risk premiums and benefit measures for generalized-expected-utility theories

Standard tools for the analysis of economic problems involving uncertainty, including risk premiums, certainty equivalents and the notions of absolute and relative risk aversion, are developed without making specific assumptions on functional form beyond the basic requirements of monotonicity, transitivity, continuity, and the presumption that individuals prefer certainty to risk. Individuals are not required to display probabilistic sophistication. The approach relies on the distance and benefit functions to characterize preferences relative to a given state-contingent vector of outcomes. The distance and benefit functions are used to derive absolute and relative risk premiums and to characterize preferences exhibiting constant absolute risk aversion (CARA) and constant relative risk aversion (CRRA). A generalization of the notion of Schur-concavity is presented. If preferences are generalized Schur concave, the absolute and relative risk premiums are generalized Schur convex, and the certainty equivalents are generalized Schur concave.

Response to price and production risk: The case of Australian wheat

A model of Australian wheat grower supply response was specified under the constraints of price and yield uncertainty, risk aversion, partial adjustment, and quadratic costs. The model was solved to obtain area planted. The results of estimation indicate that risk arising from prices and climate have had a significant influence on producer decision making. The coefficient of relative risk aversion and short-run and long-run elasticities of supply with respect to price were calculated. Wheat growers' risk premium, expected at the start of the season for exposed price and yield risk, was 2.8 percent of revenue or 10.4 percent of profit as measured by producer surplus. (C) 2000 John Wiley & Sons, Inc.

Jointly radial and translation homothetic preferences: generalized constant risk aversion

The paper identifies the structural restrictions on preferences required for them to exhibit both translation homotheticity in particular direction and radial homotheticity. The results are illustrated by an application to an asset allocation problem in the absence of riskless asset.

Invariant risk attitudes

Concepts of constant absolute risk aversion and constant relative risk aversion have proved useful in the analysis of choice under uncertainty, but are quite restrictive, particularly when they are imposed jointly. A generalization of constant risk aversion, referred to as invariant risk aversion is developed. Invariant risk aversion is closely related to the possibility of representing preferences over state-contingent income vectors in terms of two parameters, the mean and a linearly homogeneous, translation-invariant index of riskiness. The best-known index with such properties is the standard deviation. The properties of the capital asset pricing model, usually expressed in terms of the mean and standard deviation, may be extended to the case of general invariant preferences. (C) 2003 Elsevier Inc. All rights reserved.

Supermodularity and risk aversion

In this paper, we consider the relationship between supermodularity and risk aversion. We show that supermodularity of the certainty equivalent implies that the certainty equivalent of any random variable is less than its mean. We also derive conditions under which supermodularity of the certainty equivalent is equivalent to aversion to mean-preserving spreads in the sense of Rothschild and Stiglitz. (c) 2006 Elsevier B.V. All rights reserved.

Science-policy in environmental and health risk assessment: if we cannot do without, can we do better?

How can empirical evidence of adverse effects from exposure to noxious agents, which is often incomplete and uncertain, be used most appropriately to protect human health? We examine several important questions on the best uses of empirical evidence in regulatory risk management decision-making raised by the US Environmental Protection Agency (EPA)'s science-policy concerning uncertainty and variability in human health risk assessment. In our view, the US EPA (and other agencies that have adopted similar views of risk management) can often improve decision-making by decreasing reliance on default values and assumptions, particularly when causation is uncertain. This can be achieved by more fully exploiting decision-theoretic methods and criteria that explicitly account for uncertain, possibly conflicting scientific beliefs and that can be fully studied by advocates and adversaries of a policy choice, in administrative decision-making involving risk assessment. The substitution of decision-theoretic frameworks for default assumption-driven policies also allows stakeholder attitudes toward risk to be incorporated into policy debates, so that the public and risk managers can more explicitly identify the roles of risk-aversion or other attitudes toward risk and uncertainty in policy recommendations. Decision theory provides a sound scientific way explicitly to account for new knowledge and its effects on eventual policy choices. Although these improvements can complicate regulatory analyses, simplifying default assumptions can create substantial costs to society and can prematurely cut off consideration of new scientific insights (e.g., possible beneficial health effects from exposure to sufficiently low 'hormetic' doses of some agents). In many cases, the administrative burden of applying decision-analytic methods is likely to be more than offset by improved effectiveness of regulations in achieving desired goals. Because many foreign jurisdictions adopt US EPA reasoning and methods of risk analysis, it may be especially valuable to incorporate decision-theoretic principles that transcend local differences among jurisdictions.

Refining the risk-benefit equation for thrombolysis: How to identity the low risk patient before administering thrombolytic therapy

In view of the relative risk of intracranial haemorrhage and major bleeding with thrombolytic therapy, it is important ro identify as early as possible the low risk patient who may not have a net clinical benefit from thrombolysis in the setting of acute myocardial infarction. An analysis of 5434 hospital-treated patients with myocardial infarction in the Perth MONICA study showed that age below 60 and absence of previous infarction or diabetes, shock, pulmonary oedema, cardiac arrest and Q-wave or left bundle branch block on the initial ECG identified a large group of patients with a 28 day mortality of only 1%, and one year mortality of only 2%. Identification of baseline risk in this way helps refine the risk-benefit equation for thrombolytic therapy, and may help avoid unnecessary use of thrombolysis in those unlikely to benefit.

Suicide in urban New South Wales, Australia 1985-1994: Socio-economic and migrant interactions

Variation of suicide with socio-economic status (SES) in urban NSW (Australia) during 1985-1994, by sex and country or region of birth, was examined using Poisson regression analysis of vital statistics and population data (age greater than or similar to 15 yr). Quintiles of SES were defined by municipality of residence and comparisons of suicide by SES were adjusted for age and country (or region) of birth (COB), and examined by COB. Risk of suicide in females was 28% that of males for all adults and 21% for youth (age 15-24 yr). Suicide risk was lower in males from southern Europe, Middle East and Asia, and higher in northern and eastern European males, compared to the Australian-born. Risks for suicide increased significantly with decreasing SES in males, but not in females. The relationship of male suicide and SES was stronger when controlled for COB. For males, the relative risk of suicide, adjusted for age and COB, was 66% higher in the lowest SES quintile compared to the highest quintile, and 39% higher for youth (age 15-24 yr). For male suicide, the population attributable fraction for SES (less than the highest quintile) was 27%. Analysis of SES differentials in male suicide according to COB indicated a significant inverse suicide gradient in relation to SES for the Australian-born and those burn in New Zealand and the United Kingdom or fire. but not in non-English speaking COB groups, except for Asia. For Australian-born males, suicide risk was 71% higher in the lowest SES group (compared to the highest), adjusted for age. These findings indicate that SES plays an important role in male suicide rates among the Australian-born and migrants from English-speaking countries and Asia, and among youth; but not in female suicide, nor suicide in most non-English speaking migrant groups. Reduction in SES differentials through economic and social policies may reduce male suicide in lower SES groups and should be seen to be at least as important as individual level interventions. (C) 1998 Elsevier Science Ltd. All rights reserved.

Background risk in generalized expected utility theory

In this paper, it is shown that, for a wide range of risk-averse generalized expected utility preferences, independent risks are complementary, contrary to the results for expected utility preferences satisfying conditions such as proper and standard risk aversion.

Current smoking and the risk of non-fatal myocardial infarction in the WHO MONICA Project populations

Background: Cohort studies have shown that smoking has a substantial influence on coronary heart disease mortality in young people. Population based data on non-fatal events have been sparse, however. Objective: To study the impact of smoking on the risk of non-fatal acute myocardial infarction (MI) in young middle age people. Methods: From 1985 to 1994 all non-fatal MI events in the age group 35 - 64 were registered in men and women in the WHO MONICA ( multinational monitoring of trends and determinants in cardiovascular disease) project populations ( 18 762 events in men and 4047 in women from 32 populations from 21 countries). In the same populations and age groups 65 741 men and 66 717 women participated in the surveys of risk factors ( overall response rate 72%). The relative risk of non-fatal MI for current smokers was compared with non-smokers, by sex and five year age group. Results: The prevalence of smoking in people aged 35 - 39 years who experienced non-fatal MI events was 81% in men and 77% in women. It declined with increasing age to 45% in men aged 60 - 64 years and 36% in women, respectively. In the 35 - 39 years age group the relative risk of non-fatal MI for smokers was 4.9 (95% confidence interval (CI) 3.9 to 6.1) in men and 5.3 ( 95% CI 3.2 to 8.7) in women, and the population attributable fractions were 65% and 55%, respectively. Conclusions: During the study period more than half of the non-fatal MIs occurring in young middle age people can be attributed to smoking.

Prevalence of peripheral arterial disease: persistence of excess risk in former smokers

Objective: To determine the age-standardised prevalence of peripheral arterial disease (PAD) and associated risk factors, particularly smoking. Method: Design: Cross-sectional survey of a randomly selected population. Setting: Metropolitan area of Perth, Western Australia. Participants: Men aged between 65-83 years. Results: The adjusted response fraction was 77.2%. Of 4,470 men assessed, 744 were identified as having PAD by the Edinburgh Claudication Questionnaire and/or the ankle-brachial index of systolic blood pressure, yielding an age-standardised prevalence of PAD of 15.6% (95% confidence intervals (CI): 14.5%, 16.6%). The main risk factors identified in univariate analyses were increasing age, smoking current (OR=3.9, 95% CI 2.9-5.1) or former (OR=2.0, 95% CI 1.6-2.4), physical inactivity (OR=1.4, 95% CI 1.2-1.7), a history of angina (OR=2.2, 95% CI 1.8-2.7) and diabetes mellitus (OR=2.1, 95% CI 1.7-2.6). The multivariate analysis showed that the highest relative risk associated with PAD was current smoking of 25 or more cigarettes daily (OR=7.3, 95% CI 4.2-12.8). In this population, 32% of PAD was attributable to current smoking and a further 40% was attributable to past smoking by men who did not smoke currently. Conclusions: This large observational study shows that PAD is relatively common in older, urban Australian men. In contrast with its relationship to coronary disease and stroke, previous smoking appears to have a long legacy of increased risk of PAD. Implications: This research emphasises the importance of smoking as a preventable cause of PAD.

Hormone replacement therapy and breast cancer risk in California

Numerous studies have documented increased breast cancer risks with hormone replacement therapy (HRT), but these do not give a woman her specific absolute risk for the remainder of her life. This article estimates the magnitude of the effect of HRT on breast cancer incidence in California and calculates a woman's cumulative risk of breast cancer with different formulations and durations of HRT use. The effects of HRT on the underlying breast cancer incidence were estimated using the attributable fraction method, applying HRT prevalence data from the 2001 California Health Interview Survey and published rates of higher relative risk (RR) from HRT use from the Women's Health Initiative (WHI) study and Million Women's Survey (MWS). The annual number of breast cancers potentially attributable to HRT in California was estimated, along with individual cumulative risk of breast cancer for various ages to 79 years according to HRT use, duration, and formulation. Using the WHI data, 829 of 19,000 breast cancers (4.3%) in California may be attributable to HRT This figure increases to 3401 (17.4%) when the MWS RRs are applied. Use of estrogen-only HRT or short-term (approximately 5 years) use of combined HRT has a minimal effect on the cumulative risk calculated to the age of 79 years; application of the MWS data to a Californian woman commencing HRT at the age of 50 years (no HRT, 8.5%; estrogen only, 8.6%; combined, 9.1%). Prolonged (approximately 10 years) use of combined HRT increases the cumulative risk to 10.3%. This article demonstrates that HRT will generate a small additional risk of breast cancer in an individual. The reduction in perimenopausal symptoms may be considered sufficient to warrant this extra risk. However, this view needs to be balanced because the small increases in individual risk will be magnified, producing a noticeable change in population cancer caseload where HRT use is high.

Overweight and obesity increase the risk of coronary heart disease: A pooled analysis of 30 prospective studies

The importance of overweight as a risk factor for coronary heart disease (CHD) remains unsettled. We estimated the relative risk (RR) for CHD associated with underweight (body mass index, BMI < 20 kg/m2), overweight (25 – 30 kg/m2) and obesity (= 30 kg/m2), compared with normal weight (20 – 25 kg/m2) in a random effects meta-analysis of 30 prospective studies, including 389,239 healthy, predominantly Caucasian persons. We also explored sources of heterogeneity between studies and examined effects of systematic adjustment for confounding and intermediary variables. Pooled age-, sex- and smoking-adjusted RRs (95% confidence interval) for overweight, obesity and underweight compared with normal weight were 1.33 (1.24 – 1.43), 1.69 (1.44 – 1.99) and 1.01 (0.85 – 1.20), respectively. Stratified analyses showed that pooled RRs for BMI were higher for studies with longer follow-up (= vs. < 15 years) and younger populations (< vs. = 60 years). Additional adjustment for blood pressure, cholesterol levels and physical activity decreased the RR per 5 BMI units from 1.28 (1.21 – 1.34) to 1.16 (1.11 – 1.21). We conclude that overweight and obesity are associated with a substantially increased CHD risk in Caucasians, whereas underweight is not. Prevention and reduction of overweight and obesity, therefore, remain of importance for preventing CHD.