Adaptive Premiums for Evolutionary Claims in Non-Life Insurance

Rapid growth in heavy-tailed claim severity in commercial liability insurance requires insurer response by way of flexible mechanisms to update premiums. To this end in this paper a new premium principle is established for heavy-tailed claims, and its properties investigated. Risk-neutral premiums for heavy-tailed claims are consistently and unbiasedly estimated by the ratio of the first two extremes of the claims distribution. That is, the heavy-tailed risk-neutral premium has a Pareto distribution with the same tail-index as the claims distribution. Insurers must predicate premiums on larger tail-index values, if solvency is to be maintained. Additionally, the structure of heavy-tailed premiums is shown to lead to a natural model for tail-index imprecision (demonstrably inescapable in the sample sizes with which we deal). Premiums which compensate for tail-index uncertainty preserve the ratio structure of risk-neutral premiums, but make a 'prudent' adjustment which reflects the insurer's risk-profile. An example using Swiss Re's (1999) major disaster data is used to illustrate application of the methodology to the largest claims in any insurance class.Insurance Claims, Premiums, Tail-Index, Extreme Values

Minimum Variance Unbiased Maximum Likelihood Estimation of the Extreme Value Index

New results for ratios of extremes from distributions with a regularly varying tail are presented. Deriving from independence results for certain functions of order statistics, 'consecutive' ratios of extremes are shown to be independent as well as non-distribution specific. They have tractable distributions related to beta distributions. The minimum variance unbiased maximum likelihood estimator has the form of Hill's estimator. It achieves the Cramer-Rao minimum variance bound and is a function of a sufficient statistic. For small sample sizes the form of the moment generating function of the estimator shows it has a gamma distribution.Tail-index, Minimum variance unbiased, Maximum likelihood, Asymptotically normal

General Insurance Premiums When Tail Fatness Is Unknown: A Fat Premium Representation Theorem

Fat-tailed distributions are used to model claims on general insurance contracts under which extremely large claims are a very real possibility. Since estimation of the tail-fatness parameter is notoriously difficult - it is one of the major outstanding statistical/actuarial problems - methods which do not require precise knowledge are valuable. A characteristic feature of an important class of fat-tailed distributions, Pareto, is that ratios of expected values of large claims in the form {1+E[X(n)]}/{1+E[X(n-k)]} are independent of sample size. For suitably modelled uncertainty about the tail-fatness parameter, premiums to insurers with constant relative risk aversion can be represented in terms of these ratios. Premiums increase with the insurers' risk-aversion and depend upon their perception of the fattest-tailed distribution generating claims.Order statistics, constant relative risk-averse premiums, tail-fatness parameter, beta densities

The Power Principle and Tail-Fatness Uncertainty

When insurance claims are governed by fat-tailed distributions, gross uncertainty about the value of the tail-fatness index is virtually inescapable. In this paper a new premium principle (the power principle) analogous to the exponential principle for thin-tailed claims, is discussed. Pareto premiums determined under the principle have a transparent ratio structure, cater convincingly for uncertainty in the tail-fatness index, and are applicable in passage to the extremal limit, to all fat-tailed distributions in the domain of attraction of the (Frechet) extreme-value distribution. Cover can be provided for part claims if existence of the claims mean is in doubt. Stop-loss premiums are also discussed. Mathematical requirements are very modest.Exponential principle, power principle, constant risk aversion, ratio premium, stop-loss insurance

General Insurance Premiums when Tail Fatness Is Unknown: a Fat Premium Representation Theorem

Fat-tailed distributions are used to model claims on general insurance contracts under which extremely large claims are a very real possibility. Since estimation of the tail-fatness parameter is notoriously difficult - it is one of the major outstanding statistical/actuarial problems - methods which do not require precise knowledge are valuable. A characteristic feature of an important class of fat-tailed distributions, Pareto, is that ratios of expected values of large claims in the form {1+E[X(n)]}/{1+E[X(n-k)]} are independent of sample size. For suitably modelled uncertainty about the tail-fatness parameter, premiums to insurers with constant relative risk aversion can be represented in terms of these ratios. Premiums increase with the insurers' risk-aversion and depend upon their perception of the fattest-tailed distribution generating claims

Impact of Computer Experience on the Viability and Repeatablity of the Moorfields Motion Displacement Test in a Developing and Underserved African Setting

Background: The current study was designed to explore the effect of computer experience on the viability and testretest repeatability of the Moorfields Motion Displacement Test (MMDT), a novel computer-driven glaucoma screening device, in an African community setting. Methods: 164 healthy subjects were recruited from a semi-rural Mozambican environment, and stratified according to computer experience (computer naïve: n=85, computer familiar: n=79). A suprathreshold screening test algorithm was employed, and the global probability of true damage (GPTD), testing time (TT) and false positive (FP) response rate were recorded. The visual field test was conducted twice on the same eye, and results compared to determine intra-sessional repeatability. Results: No inter-group differences in GPTD or TT (p\u3e0.05) were observed between computer subgroups, although FP response rate was significantly higher among computer naïve subjects (p=0.00 for both tests). No inter-sessional differences were observed for GPTD, TT and FP (p\u3e0.05 for all) for either subgroup. A statistically significant positive correlation was found between repeat GPTD, TT and FP measures for all subgroups (

Validation of a short form Wisconsin Upper Respiratory Symptom Survey (WURSS-21)

<p>Abstract</p> <p>Background</p> <p>The Wisconsin Upper Respiratory Symptom Survey (WURSS) is an illness-specific health-related quality-of-life questionnaire outcomes instrument.</p> <p>Objectives</p> <p>Research questions were: 1) How well does the WURSS-21 assess the symptoms and functional impairments associated with common cold? 2) How well can this instrument measure change over time (responsiveness)? 3) What is the minimal important difference (MID) that can be detected by the WURSS-21? 4) What are the descriptive statistics for area under the time severity curve (AUC)? 5) What sample sizes would trials require to detect MID or AUC criteria? 6) What does factor analysis tell us about the underlying dimensional structure of the common cold? 7) How reliable are items, domains, and summary scores represented in WURSS? 8) For each of these considerations, how well does the WURSS-21 compare to the WURSS-44, Jackson, and SF-8?</p> <p>Study Design and Setting</p> <p>People with Jackson-defined colds were recruited from the community in and around Madison, Wisconsin. Participants were enrolled within 48 hours of first cold symptom and monitored for up to 14 days of illness. Half the sample filled out the WURSS-21 in the morning and the WURSS-44 in the evening, with the other half reversing the daily order. External comparators were the SF-8, a 24-hour recall general health measure yielding separate physical and mental health scores, and the eight-item Jackson cold index, which assesses symptoms, but not functional impairment or quality of life.</p> <p>Results</p> <p>In all, 230 participants were monitored for 2,457 person-days. Participants were aged 14 to 83 years (mean 34.1, SD 13.6), majority female (66.5%), mostly white (86.0%), and represented substantive education and income diversity. WURSS-21 items demonstrated similar performance when embedded within the WURSS-44 or in the stand-alone WURSS-21. Minimal important difference (MID) and Guyatt's responsiveness index were 10.3, 0.71 for the WURSS-21 and 18.5, 0.75 for the WURSS-44. Factorial analysis suggested an eight dimension structure for the WURSS-44 and a three dimension structure for the WURSS-21, with composite reliability coefficients ranging from 0.87 to 0.97, and Cronbach's alpha ranging from 0.76 to 0.96. Both WURSS versions correlated significantly with the Jackson scale (W-21 R = 0.85; W-44 R = 0.88), with the SF-8 physical health (W-21 R = -0.79; W-44 R = -0.80) and SF-8 mental health (W-21 R = -0.55; W-44 R = -0.60).</p> <p>Conclusion</p> <p>The WURSS-44 and WURSS-21 perform well as illness-specific quality-of-life evaluative outcome instruments. Construct validity is supported by the data presented here. While the WURSS-44 covers more symptoms, the WURSS-21 exhibits similar performance in terms of reliability, responsiveness, importance-to-patients, and convergence with other measures.</p

Anxiety, emotional processing and depression in people with multiple sclerosis.

BACKGROUND: Despite the high comorbidity of anxiety and depression in people with multiple sclerosis (MS), little is known about their inter-relationships. Both involve emotional perturbations and the way in which emotions are processed is likely central to both. The aim of the current study was to explore relationships between the domains of mood, emotional processing and coping and to analyse how anxiety affects coping, emotional processing, emotional balance and depression in people with MS. METHODS: A cross-sectional questionnaire study involving 189 people with MS with a confirmed diagnosis of MS recruited from three French hospitals. Study participants completed a battery of questionnaires encompassing the following domains: i. anxiety and depression (Hospital Anxiety and Depression Scale (HADS)); ii. emotional processing (Emotional Processing Scale (EPS-25)); iii. positive and negative emotions (Positive and Negative Emotionality Scale (EPN-31)); iv. alexithymia (Bermond-Vorst Alexithymia Questionnaire) and v. coping (Coping with Health Injuries and Problems-Neuro (CHIP-Neuro) questionnaire. Relationships between these domains were explored using path analysis. RESULTS: Anxiety was a strong predictor of depression, in both a direct and indirect way, and our model explained 48% of the variance of depression. Gender and functional status (measured by the Expanded Disability Status Scale) played a modest role. Non-depressed people with MS reported high levels of negative emotions and low levels of positive emotions. Anxiety also had an indirect impact on depression via one of the subscales of the Emotional Processing Scale ("Unregulated Emotion") and via negative emotions (EPN-31). CONCLUSIONS: This research confirms that anxiety is a vulnerability factor for depression via both direct and indirect pathways. Anxiety symptoms should therefore be assessed systematically and treated in order to lessen the likelihood of depression symptoms