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.

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.

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.

Absolute risk of breast cancer for Australian women with a family history

Background: The purpose of the present paper was to estimate the absolute risk of breast cancer over the remainder of a lifetime in Australian women with different categories of family history. Methods: Age-specific breast cancer incidence rates were adjusted for screening effects, and rates in those with no family history were estimated using the attributable fraction (AF). Relative risks from a published meta-analysis were applied to obtain incidence rates for different categories of family history, and age-specific incidence was converted to cumulative risk of breast cancer. The risk estimates were based upon Australian population statistics and published relative risks. Breast cancer incidence was from New South Wales women for 1996. The AF was calculated using prevalence of a family history of breast cancer from data on Queensland women. The cumulative absolute risk of breast cancer was calculated from decade and mid-decade ages to age 79 years, not adjusted for competing causes of death. Results: Lifetime risk is approximately 8.6% (1 in 12) for the general population and 7.8% (1 in 13) for those without a family history. Women with one relative affected have lifetime risks of 1 in 6-8 and those with two relatives affected have lifetime risks of 1 in 4-6. The cumulative residual lifetime risk decreases with advancing age; by age 60 years all groups with only one relative affected have well above a 90% probability of not developing breast cancer to age 79 years. Conclusions: These Australian risk statistics are useful for public information and in the clinical setting. Risks given here apply to women with average breast cancer risk from other risk factors.

Quality of diabetes care and coronary heart disease absolute risk in patients with type 2 diabetes mellitus in Australian general practice

Objective: To examine the quality of diabetes care and prevention of cardiovascular disease (CVD) in Australian general practice patients with type 2 diabetes and to investigate its relationship with coronary heart disease absolute risk (CHDAR). Methods: A total of 3286 patient records were extracted from registers of patients with type 2 diabetes held by 16 divisions of general practice (250 practices) across Australia for the year 2002. CHDAR was estimated using the United Kingdom Prospective Diabetes Study algorithm with higher CHDAR set at a 10 year risk of >15%. Multivariate multilevel logistic regression investigated the association between CHDAR and diabetes care. Results: 47.9% of diabetic patient records had glycosylated haemoglobin (HbA1c) >7%, 87.6% had total cholesterol >= 4.0 mmol/l, and 73.8% had blood pressure (BP) >= 130/85 mm Hg. 57.6% of patients were at a higher CHDAR, 76.8% of whom were not on lipid modifying medication and 66.2% were not on antihypertensive medication. After adjusting for clustering at the general practice level and age, lipid modifying medication was negatively related to CHDAR (odds ratio (OR) 0.84) and total cholesterol. Antihypertensive medication was positively related to systolic BP but negatively related to CHDAR (OR 0.88). Referral to ophthalmologists/optometrists and attendance at other health professionals were not related to CHDAR. Conclusions: At the time of the study the diabetes and CVD preventive care in Australian general practice was suboptimal, even after a number of national initiatives. The Australian Pharmaceutical Benefits Scheme (PBS) guidelines need to be modified to improve CVD preventive care in patients with type 2 diabetes.

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.

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.

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.

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.

Long-term risk stratification for survivors of acute coronary syndromes - Results from the long-term intervention with pravastatin in ischemic disease (LIPID) study

OBJECTIVES We developed a prognostic strategy for quantifying the long-term risk of coronary heart disease (CHD) events in survivors of acute coronary syndromes (ACS). BACKGROUND Strategies for quantifying long-term risk of CHD events have generally been confined to primary prevention settings. The Long-term Intervention with Pravastatin in Ischemic Disease (LIPID) study, which demonstrated that pravastatin reduces CHD events in ACS survivors with a broad range of cholesterol levels, enabled assessment of long-term prognosis in a secondary prevention setting. METHODS Based on outcomes in 8,557 patients in the LIPID study, a multivariate risk factor model was developed for prediction of CHD death or nonfatal myocardial infarction. Prognostic indexes were developed based on the model, and low-, medium-, high- and very high-risk groups were defined by categorizing the prognostic indexes. RESULTS In addition to pravastatin treatment, the independently significant risk factors included: total and high density lipoprotein cholesterol, age, gender, smoking status, qualifying ACS, prior coronary revascularization, diabetes mellitus, hypertension and prior stroke. Pravastatin reduced coronary event rates in each risk level, and the relative risk reduction did not vary significantly between risk levels. The predicted five-year coronary event rates ranged from 5% to 19% for those assigned pravastatin and from 6.4% to 23.6% fur those assigned placebo. CONCLUSIONS Long-term prognosis of ACS survivors varied substantially according to conventional risk factor profile. Pravastatin reduced coronary risk within all risk levels; however, absolute risk remained high in treated patients with unfavorable profiles. Our risk stratification strategy enables identification of ACS survivors who remain at very high risk despite statin therapy. CT Am Coil Cardiol 2001;38:56-63) (C) 2001 by the American College of Cardiology.

Price stabilization and the risk-averse firm

An analytically simple and tractable approach to firm-level welfare analysis of complete and partial mean-preserving price stabilization for producers with general risk-averse preferences facing a stochastic technology is developed. Necessary and sufficient conditions for price stabilization to be welfare enhancing are derived under different assumptions of the producer's preferences and the producer's technology. Existing stabilization results for the risk-averse firm are shown to be corollaries of these more general results.

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.

Production under uncertainty and choice under uncertainty in the emergence of generalized expected utility theory

This paper presents a personal view of the interaction between the analysis of choice under uncertainty and the analysis of production under uncertainty. Interest in the foundations of the theory of choice under uncertainty was stimulated by applications of expected utility theory such as the Sandmo model of production under uncertainty. This interest led to the development of generalized models including rank-dependent expected utility theory. In turn, the development of generalized expected utility models raised the question of whether such models could be used in the analysis of applied problems such as those involving production under uncertainty. Finally, the revival of the state-contingent approach led to the recognition of a fundamental duality between choice problems and production problems.