Beyond Value-at-Risk : GlueVaR Distortion Risk Measures

We propose a new family of risk measures, called GlueVaR, within the class of distortion risk measures. Analytical closed-form expressions are shown for the most frequently used distribution functions in financial and insurance applications. The relationship between Glue-VaR, Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) is explained. Tail-subadditivity is investigated and it is shown that some GlueVaR risk measures satisfy this property. An interpretation in terms of risk attitudes is provided and a discussion is given on the applicability in non-financial problems such as health, safety, environmental or catastrophic risk management

The use of flexible quantile-based measures in risk assessment

A new family of distortion risk measures -GlueVaR- is proposed in Belles- Sampera et al. -2013- to procure a risk assessment lying between those provided by common quantile-based risk measures. GlueVaR risk measures may be expressed as a combination of these standard risk measures. We show here that this relationship may be used to obtain approximations of GlueVaR measures for general skewed distribution functions using the Cornish-Fisher expansion. A subfamily of GlueVaR measures satisfies the tail-subadditivity property. An example of risk measurement based on real insurance claim data is presented, where implications of tail-subadditivity in the aggregation of risks are illustrated.

The connection between distortion risk measures and ordered weighted averaging operators

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and finite random variables is presented. This connection offers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.

Monitoring Fatigue Status with HRV Measures in Elite Athletes : An Avenue Beyond RMSSD?

Among the tools proposed to assess the athlete's "fatigue," the analysis of heart rate variability (HRV) provides an indirect evaluation of the settings of autonomic control of heart activity. HRV analysis is performed through assessment of time-domain indices, the square root of the mean of the sum of the squares of differences between adjacent normal R-R intervals (RMSSD) measured during short (5 min) recordings in supine position upon awakening in the morning and particularly the logarithm of RMSSD (LnRMSSD) has been proposed as the most useful resting HRV indicator. However, if RMSSD can help the practitioner to identify a global "fatigue" level, it does not allow discriminating different types of fatigue. Recent results using spectral HRV analysis highlighted firstly that HRV profiles assessed in supine and standing positions are independent and complementary; and secondly that using these postural profiles allows the clustering of distinct sub-categories of "fatigue." Since, cardiovascular control settings are different in standing and lying posture, using the HRV figures of both postures to cluster fatigue state embeds information on the dynamics of control responses. Such, HRV spectral analysis appears more sensitive and enlightening than time-domain HRV indices. The wealthier information provided by this spectral analysis should improve the monitoring of the adaptive training-recovery process in athletes.

Monitoring Fatigue Status with HRV Measures in Elite Athletes: An Avenue Beyond RMSSD?

Among the tools proposed to assess the athlete's "fatigue," the analysis of heart rate variability (HRV) provides an indirect evaluation of the settings of autonomic control of heart activity. HRV analysis is performed through assessment of time-domain indices, the square root of the mean of the sum of the squares of differences between adjacent normal R-R intervals (RMSSD) measured during short (5 min) recordings in supine position upon awakening in the morning and particularly the logarithm of RMSSD (LnRMSSD) has been proposed as the most useful resting HRV indicator. However, if RMSSD can help the practitioner to identify a global "fatigue" level, it does not allow discriminating different types of fatigue. Recent results using spectral HRV analysis highlighted firstly that HRV profiles assessed in supine and standing positions are independent and complementary; and secondly that using these postural profiles allows the clustering of distinct sub-categories of "fatigue." Since, cardiovascular control settings are different in standing and lying posture, using the HRV figures of both postures to cluster fatigue state embeds information on the dynamics of control responses. Such, HRV spectral analysis appears more sensitive and enlightening than time-domain HRV indices. The wealthier information provided by this spectral analysis should improve the monitoring of the adaptive training-recovery process in athletes.

A relational approach to the geography of innovation: a typology of regions

The aim of this study was to devise a method for computing a composite indicator that measures the regional degree of exposure to external knowledge sources. On the basis of this indicator, we propose a typology of regions according to their potential capacity to access extra-local items of knowledge, which might help them to recombine complementary elements of such an asset to produce a higher number of new ideas. Building on various research streams that have been relatively independent to date, we summarize a non-exhaustive instrumental list of recent studies that motivates our approach and the construction of our complex indicator, which can be used to appraise the extent to which each region is in an optimal position to access external innovative resources.

Correcting Interdevice Bias of Horizontal White-to-White and Sulcus-to-Sulcus Measures Used for Implantable Collamer Lens Sizing.

PURPOSE: To assess the agreement and repeatability of horizontal white-to-white (WTW) and horizontal sulcus-to-sulcus (STS) diameter measurements and use these data in combination with available literature to correct for interdevice bias in preoperative implantable collamer lens (ICL) size selection. DESIGN: Interinstrument reliability and bias assessment study. METHODS: A total of 107 eyes from 56 patients assessed for ICL implantation at our institution were included in the study. This was a consecutive series of all patients with suitable available data. The agreement and bias between WTW (measured with the Pentacam and BioGraph devices) and STS (measured with the HiScan device) were estimated. RESULTS: The mean spherical equivalent was -8.93 ± 5.69 diopters. The BioGraph measures of WTW were wider than those taken with the Pentacam (bias = 0.26 mm, P < .01), and both horizontal WTW measures were wider than the horizontal STS measures (bias >0.91 mm, P < .01). The repeatability (Sr) of STS measured with the HiScan was 0.39 mm, which was significantly reduced (Sr = 0.15 mm) when the average of 2 measures was used. Agreement between the horizontal WTW measures and horizontal STS estimates when bias was accounted for was г = 0.54 with the Pentacam and г = 0.64 with the BioGraph. CONCLUSIONS: Large interdevice bias was observed for WTW and STS measures. STS measures demonstrated poor repeatability, but the average of repeated measures significantly improved repeatability. In order to conform to the US Food and Drug Administration's accepted guidelines for ICL sizing, clinicians should be aware of and account for the inconsistencies between devices.

Many valued algebraic structures as measures of comparison

This thesis studies the properties and usability of operators called t-norms, t-conorms, uninorms, as well as many valued implications and equivalences. Into these operators, weights and a generalized mean are embedded for aggregation, and they are used for comparison tasks and for this reason they are referred to as comparison measures. The thesis illustrates how these operators can be weighted with a differential evolution and aggregated with a generalized mean, and the kinds of measures of comparison that can be achieved from this procedure. New operators suitable for comparison measures are suggested. These operators are combination measures based on the use of t-norms and t-conorms, the generalized 3_-uninorm and pseudo equivalence measures based on S-type implications. The empirical part of this thesis demonstrates how these new comparison measures work in the field of classification, for example, in the classification of medical data. The second application area is from the field of sports medicine and it represents an expert system for defining an athlete's aerobic and anaerobic thresholds. The core of this thesis offers definitions for comparison measures and illustrates that there is no actual difference in the results achieved in comparison tasks, by the use of comparison measures based on distance, versus comparison measures based on many valued logical structures. The approach has been highly practical in this thesis and all usage of the measures has been validated mainly by practical testing. In general, many different types of operators suitable for comparison tasks have been presented in fuzzy logic literature and there has been little or no experimental work with these operators.

Tests of International Asset Pricing Models in Scandinavian Stock Markets

This thesis examines whether global, local and exchange risks are priced in Scandinavian countries’ equity markets by using conditional international asset pricing models. The employed international asset pricing models are the world capital asset pricing model, the international asset pricing model augmented with the currency risk, and the partially segmented model augmented with the currency risk. Moreover, this research traces estimated equity risk premiums for the Scandinavian countries. The empirical part of the study is performed using generalized method of moments approach. Monthly observations from February 1994 to June 2007 are used. Investors’ conditional expectations are modeled using several instrumental variables. In order to keep system parsimonious the prices of risk are assumed to be constant whereas expected returns and conditional covariances vary over time. The empirical findings of this thesis suggest that the prices of global and local market risk are priced in the Scandinavian countries. This indicates that the Scandinavian countries are mildly segmented from the global markets. Furthermore, the results show that the exchange risk is priced in the Danish and Swedish stock markets when the partially segmented model is augmented with the currency risk factor.

View-dependent information theory quality measures for pixel sampling and scene discretization in flatland

In this paper, we present view-dependent information theory quality measures for pixel sampling and scene discretization in flatland. The measures are based on a definition for the mutual information of a line, and have a purely geometrical basis. Several algorithms exploiting them are presented and compare well with an existing one based on depth differences