Risk measure index tracking model

Lateral Control for UAVs using Sliding Mode Technique

Closed-Form Solutions for Worst-Case Law Invariant Risk Measures with Application to Robust Portfolio Optimization

The SynchronyTM Respiratory Tracking System (SRTS) component of the CyberKnife® Robotic Radiosurgery System (Accuray, Inc., Sunnyvale CA) enables real-time tracking of moving targets by modeling the correlation between the targets and external surrogate light-emitting diode (LED) markers placed on the patient's chest. Previous studies reported some cases with respiratory phase shifts between lung tumor and chest wall motions. In this study, the impacts of respiratory phase shifts on the motion-tracking accuracy of the SRTS were investigated. A plastic scintillator was used to detect the position of the x-ray beams. The scintillation light was recorded using a camera in a dark room. A moving phantom moved a U-shaped frame on the scintillator with a 4th power of sinusoidal functions. Three metallic markers for motion tracking and four fluorescent tapes were attached to the frame. The fluorescent tapes were used to identify phantom position and respiratory phase for each video frame. The beam positions collected, when considered relative to the phantom motion, represent the degree of tracking error. Beam position was calculated by adding error value to phantom position. Motions with respiratory phase shifts between the target and an extra stage mimicking chest wall motion were also tested for LED markers. Log files of the SRTS were analyzed to evaluate correlation errors. When target and LED marker motions were synchronized with a respiratory cycle of 4s, the maximum tracking errors for 90% and 95% of beam-on time were 1.0mm and 1.2mm, respectively. The frequency of tracking errors increased when LED marker motion phase preceded target motion. Tracking errors that corresponded to 90% beam-on time were within 2.4mm for 5-15% of phase shifts. In contrast, the tracking errors were very large when the LED marker delayed to the target motions; the maximum errors of 90% beam-on time were 3.0, 3.8, and 7.5mm for 5%, 10%, and 15% of phase shifts, respectively. The patterns of the tracking errors derived from the scintillation light were very similar to those of the correlation data of the SRTS derived from the log files, indicating that the tracking errors caused mainly due to the errors in modeling the correlation data. With long respiratory cycle of 6s, the tracking errors were significantly decreased; the maximum tracking errors for 95% beam-on time were 1.6mm and 2.2mm for early and delayed LED motion. We have investigated the motion-tracking accuracy of the CyberKnife SRTS for cases with the respiratory phase shift between the target and the LED marker. The maximum tracking errors for 90% probability were within 2.4mm when the target delays to the LED markers. When LED marker delays, however, very large tracking errors were observed. With a long respiratory cycle, the tracking errors were greatly improved to less than 2.2mm. Coaching slow breathing will be useful for accurate motion tracking radiotherapy.

Chapter 11: Terrestrial vertebrates

A kind of new time-weighted nonnegative lasso index-tracking model and its application

Qualified market risk management of asset and liability portfolios or trading activities is of key importance for banks and financial institutions. It is not only about quantitative measurement of the risks, but also about organizational and regulatory principles. Besides relatively simple market risk measures, we will define and explain various approaches to Value at Risk (VaR) and Conditional VaR estimation and backtesting. The two risk measures are used for day-to-day management as well as key regulatory capital concepts, or as tools of strategic risk management based on economic capital allocation. Market risk management, in particular in case of OTC derivatives, is also closely related to the counterparty credit risk management and measurement in terms of CVA (Credit Valuation Adjustment) that will be in detail discussed in the last section of this chapter.

The theory and practice of risk measurement provides a point of intersection between risk management, economic theories of choice under risk, financial economics, and actuarial pricing theory. This article provides a review of these interrelationships, from the perspective of an insurance company seeking to price the risks that it underwrites. We examine three distinct approaches to insurance risk pricing, all being contingent on the concept of risk measures. Risk measures can be interpreted as representations of risk orderings, as well as absolute (monetary) quantifiers of risk. The first approach can be called an "axiomatic" one, whereby the price for risks is calculated according to a functional determined by a set of desirable properties. The price of a risk is directly interpreted as a risk measure and may be induced by an economic theory of price under risk. The second approach consists in contextualizing the considerations of the risk bearer by embedding them in the market where risks are traded. Prices are calculated by equilibrium arguments, where each economic agent's optimization problem follows from the minimization of a risk measure. Finally, in the third approach, weaknesses of the equilibrium approach are addressed by invoking alternative valuation techniques, the leading paradigm among which is arbitrage pricing. Such models move the focus from individual decision takers to abstract market price systems and are thus more parsimonious in the amount of information that they require. In this context, risk measures, instead of characterizing individual agents, are used for determining the set of price systems that would be viable in a market.

We investigate the relation between various alternative risk measures and future daily returns using a sample of firms over the 1988-2009 time period. Previous research indicates that returns are not normally distributed and that investors seem to care more about downside risk than total risk. Motivated by these findings and mixed empirical evidence supporting theoretical positive risk-return relationship, we model the relation between future returns and risk measures and investigate the following questions: (1) Are investors compensated for total risk and/or asymmetric measures of risk? (2) How does the degree of risk aversion in the lower tail of the return distribution impact the predictability of future returns? (3) Is upside risk or downside risk a better predictor of future returns? We find that, although investors seem to be compensated for total risk, measures of downside risk, such as the lower partial moment, are better at explaining future returns. Further, when comparing downside risk to upside risk, we find that investors are more concerned about downside risk. That is, downside risk is a better predictor of future returns. Our results are robust to the addition of traditional control variables, including size, book-to-market ratio of equity (B/M), leverage, and market risk measures, including beta, downside beta and co-skewness. Our findings are an important contribution to the literature as we document a positive risk-return relationship, using both total and asymmetric measures of risk.

<p>Risk measures have been studied for several decades in the financial literature. Mathematically, a risk measure is a mapping from a class of random variables defined on some space X to the (extended) real line. It is difficult to give a reliable assessment of financial risk without a suitable model space X where the financial position lies there. </p> <p>In this work, we assume the domain <em>X</em> for the risk measure <em>ρ : X</em> → (−∈,∈] is a subset of <em>L</em><sup>1</sup> that contains the space of simple random variables L and has the Fatou property. We focus on dilatation monotonicity as desirable preferences of the decision-maker over risks. We discuss continuity properties of dilatation monotone risk measures on <em>X</em>. We prove that on a non-atomic probability space, every dilatation monotone convex risk measure on <em>X</em> can extend uniquely to a σ(<em>L</em><sup>1</sup>,L)-lower semicontinuous dilatation monotone convex risk measure. Our findings complement extension and continuity results for (quasi)convex law-invariant functionals. </p> <p>In the second part of this thesis, we overview various properties of the Haezendonck–Goovaerts risk measure as a dilatation monotone risk measure. In the special case <em>Φ(x) = x</em><sup><em>2</em></sup>, we develop an explicit expression for the Haezendonck–Goovaerts risk measure when the risk variable <em>X</em> follows some specific distributions and propose an empirical algorithm to estimate this risk measure. Moreover, we investigate the performance of some members of this class of risk measures on real data as a possible application of the Haezendonck-Goovaerts risk measure. </p>

Portfolio management using lower partial risk (downside risk) measures is attracting more attention of practitioners in recent years. The purpose of this paper is to review important characteristics of these riskmeasures and conduct simulation using four alternative measures, lower semi-variance, lower semi-absolute deviation, first order below targetrisk and conditional value-at-risk.We will show that these risk measures are useful to control downside risk whenthe distribution of assets is non-symmetric. Further, we will propose a computational scheme to resolve the difficultyassociated with solving a large dense linear programming problems resulting from these models. We will demonstrate that this method can in fact solve problems consisting of104 assets and 105 scenarios within a practical amount of CPU time.

This article proposes intraday high‐frequency risk (HFR) measures for market risk in the case of irregularly spaced high‐frequency data. In this context, we distinguish three concepts of value‐at‐risk (VaR): the total VaR, the marginal (or per‐time‐unit) VaR and the instantaneous VaR. Since the market risk is obviously related to the duration between two consecutive trades, these measures are completed with a duration risk measure, i.e. the time‐at‐risk (TaR). We propose a forecasting procedure for VaR and TaR for each trade or other market microstructure event. Subsequently, we perform a backtesting procedure specifically designed to assess the validity of the VaR and TaR forecasts on irregularly spaced data. The performance of the HFR measure is illustrated in an empirical application for two stocks (Bank of America and Microsoft) and an exchange‐traded fund based on Standard & Poor's 500 index. We show that the intraday HFR forecasts capture accurately the volatility and duration dynamics for these three assets. Copyright © 2015 John Wiley & Sons, Ltd.

PurposeThis study aims to examine the ability of clean energy stocks to provide cover for investors against market risks related to climate change and disturbances in the oil market.Design/methodology/approachThe study adopts the feasible quasi generalized least squares technique to estimate a predictive model based on Westerlund and Narayan’s (2015) approach to evaluating the hedging effectiveness of clean energy stocks. The out-of-sample forecast evaluations of the oil risk-based and climate risk-based clean energy predictive models are explored using Clark and West’s model (2007) and a modified Diebold & Mariano forecast evaluation test for nested and non-nested models, respectively.FindingsThe study finds ample evidence that clean energy stocks may hedge against oil market risks. This result is robust to alternative measures of oil risk and holds when applied to data from the COVID-19 pandemic. In contrast, the hedging effectiveness of clean energy against climate risks is limited to 4 of the 6 clean energy indices and restricted to climate risk measured with climate policy uncertainty.Originality/valueThe study contributes to the literature by providing extensive analysis of hedging effectiveness of several clean energy indices (global, the United States (US), Europe and Asia) and sectoral clean energy indices (solar and wind) against oil market and climate risks using various measures of oil risk (WTI (West Texas intermediate) and Brent volatility) and climate risk (climate policy uncertainty and energy and environmental regulation) as predictors. It also conducts forecast evaluations of the clean energy predictive models for nested and non-nested models.

Risk management plays a critical part in every organization‘s profit maximization through risk cost minimization for wise protection, which cannot be overstated. Risk mitigation (rmt), risk monitoring (rmn), risk management environment, procedure, and policies (epp), and risk measurement (rme) in relation to the profitability of the insurance industry in Nigeria were randomly selected from a wellstructured 5-point Likert scale questionnaire ranging rom ‘5 strongly agree‘ to ‘4 agree‘, ‘3 undecided‘ to ‘1 strongly disagree‘. Using the StataSE 14 statistical software, one hundred and twenty (120) questionnaires were recovered from respondents, accounting for 83 percent of the total questionnaires sent using the multiple regression statistical methodology. Risk reduction and risk monitoring have a considerable impact on the profitability of insurance companies in Nigeria, according to the findings. As a result, it concluded that risk mitigation and monitoring are important factors in determining industry profitability, and those insurance regulators should work to ensure that risk identification, assessment, measurement, and control mechanisms are implemented in accordance with best global practices in order to avoid financial crises and improve insurance performance.

This paper presents sliding mode based lateral control for UAVs using piecewise linear sliding surface. A single linear surface is replaced by piecewise linear sliding surface to ensure the performance during small track errors or divergence and a bounded heading error in the case of large track error, thus avoiding the actuator saturations. Stability of the proposed sliding surface is analyzed with piecewise analytical solution of the proposed sliding surface. The proposed scheme uses only the readily available sensor information that is lateral track error and heading error angle and no succeeding mission information are required here. The proposed scheme is implemented on the 6-degrees-of-freedom (6-dof) simulation and different cases of large and small track errors are simulated in the presence/absence of wind to successfully validate the proposed control scheme.

Residual risk, the ongoing appreciable risk of major cardiovascular events (MCVE) in statin-treated patients who have achieved evidence-based lipid goals, remains a concern among cardiologists. Factors that contribute to this continuing risk are atherogenic non-low-density lipoprotein (LDL) particles and atherogenic processes unrelated to LDL cholesterol, including other risk factors, the inherent properties of statin drugs, and patient characteristics, ie, genetics and behaviors. In addition, providers, health care systems, the community, public policies, and the environment play a role. Major statin studies suggest an average 28% reduction in LDL cholesterol and a 31% reduction in relative risk, leaving a residual risk of about 69%. Incomplete reductions in risk, and failure to improve conditions that create risk, may result in ongoing progression of atherosclerosis, with new and recurring lesions in original and distant culprit sites, remodeling, arrhythmias, rehospitalizations, invasive procedures, and terminal disability. As a result, identification of additional agents to reduce residual risk, particularly administered together with statin drugs, has been an ongoing quest. The current model of atherosclerosis involves many steps during which disease may progress independently of guideline-defined elevations in LDL cholesterol. Differences in genetic responsiveness to statin therapy, differences in ability of the endothelium to regenerate and repair, and differences in susceptibility to nonlipid risk factors, such as tobacco smoking, hypertension, and molecular changes associated with obesity and diabetes, may all create residual risk. A large number of inflammatory and metabolic processes may also provide eventual therapeutic targets to lower residual risk. Classically, epidemiologic and other evidence suggested that raising high-density lipoprotein (HDL) cholesterol would be cardioprotective. When LDL cholesterol is aggressively lowered to targets, low HDL cholesterol levels are still inversely related to MCVE. The efflux capacity, or ability to relocate cholesterol out of macrophages, is believed to be a major antiatherogenic mechanism responsible for reduction in MCVE mediated in part by healthy HDL. HDL cholesterol is a complex molecule with antioxidative, anti-inflammatory, anti-thrombotic, antiplatelet, and vasodilatory properties, among which is protection of LDL from oxidation. HDL-associated paraoxonase-1 has a major effect on endothelial function. Further, HDL promotes endothelial repair and progenitor cell health, and supports production of nitric oxide. HDL from patients with cardiovascular disease, diabetes, and autoimmune disease may fail to protect or even become proinflammatory or pro-oxidant. Mendelian randomization and other clinical studies in which raising HDL cholesterol has not been beneficial suggest that high plasma levels do not necessarily reduce cardiovascular risk. These data, coupled with extensive preclinical information about the functional heterogeneity of HDL, challenge the “HDL hypothesis”, ie, raising HDL cholesterol per se will reduce MCVE. After the equivocal AIM-HIGH (Atherothrombosis Intervention in Metabolic Syndrome With Low HDL/High Triglycerides: Impact on Global Health Outcomes) study and withdrawal of two major cholesteryl ester transfer protein compounds, one for off-target adverse effects and the other for lack of efficacy, development continues for two other agents, ie, anacetrapib and evacetrapib, both of which lower LDL cholesterol substantially. The negative but controversial HPS2-THRIVE (the Heart Protection Study 2-Treatment of HDL to Reduce the Incidence of Vascular Events) trial casts further doubt on the HDL cholesterol hypothesis. The growing impression that HDL functionality, rather than abundance, is clinically important is supported by experimental evidence highlighting the conditional pleiotropic actions of HDL. Non-HDL cholesterol reflects the cholesterol in all atherogenic particles containing apolipoprotein B, and has outperformed LDL cholesterol as a lipid marker of cardiovascular risk and future mortality. In addition to including a measure of residual risk, the advantages of using non-HDL cholesterol as a primary lipid target are now compelling. Reinterpretation of data from the Treating to New Targets study suggests that better control of smoking, body weight, hypertension, and diabetes will help lower residual risk. Although much improved, control of risk factors other than LDL cholesterol currently remains inadequate due to shortfalls in compliance with guidelines and poor patient adherence. More efficient and greater use of proven simple therapies, such as aspirin, beta-blockers, angiotensin-converting enzyme inhibitors and angiotensin II receptor blockers, combined with statin therapy, may be more fruitful in improving outcomes than using other complex therapies. Comprehensive, intensive, multimechanistic, global, and national programs using primordial, primary, and secondary prevention to lower the total level of cardiovascular risk are necessary.