Análise de portfólio: uma perspectiva bayesiana

Este trabalho tem com objetivo abordar o problema de alocação de ativos (análise de portfólio) sob uma ótica Bayesiana. Para isto foi necessário revisar toda a análise teórica do modelo clássico de média-variância e na sequencia identificar suas deficiências que comprometem sua eficácia em casos reais. Curiosamente, sua maior deficiência não esta relacionado com o próprio modelo e sim pelos seus dados de entrada em especial ao retorno esperado calculado com dados históricos. Para superar esta deficiência a abordagem Bayesiana (modelo de Black-Litterman) trata o retorno esperado como uma variável aleatória e na sequência constrói uma distribuição a priori (baseado no modelo de CAPM) e uma distribuição de verossimilhança (baseado na visão de mercado sob a ótica do investidor) para finalmente aplicar o teorema de Bayes tendo como resultado a distribuição a posteriori. O novo valor esperado do retorno, que emerge da distribuição a posteriori, é que substituirá a estimativa anterior do retorno esperado calculado com dados históricos. Os resultados obtidos mostraram que o modelo Bayesiano apresenta resultados conservadores e intuitivos em relação ao modelo clássico de média-variância.

The prognostic value of a nomogram for exercise capacity in women

BACKGROUND: Recent studies have demonstrated that exercise capacity is an independent predictor of mortality in women. Normative values of exercise capacity for age in women have not been well established. Our objectives were to construct a nomogram to permit determination of predicted exercise capacity for age in women and to assess the predictive value of the nomogram with respect to survival. METHODS: A total of 5721 asymptomatic women underwent a symptom-limited, maximal stress test. Exercise capacity was measured in metabolic equivalents (MET). Linear regression was used to estimate the mean MET achieved for age. A nomogram was established to allow the percentage of predicted exercise capacity to be estimated on the basis of age and the exercise capacity achieved. The nomogram was then used to determine the percentage of predicted exercise capacity for both the original cohort and a referral population of 4471 women with cardiovascular symptoms who underwent a symptom-limited stress test. Survival data were obtained for both cohorts, and Cox survival analysis was used to estimate the rates of death from any cause and from cardiac causes in each group. RESULTS: The linear regression equation for predicted exercise capacity (in MET) on the basis of age in the cohort of asymptomatic women was as follows: predicted MET = 14.7 - (0.13 x age). The risk of death among asymptomatic women whose exercise capacity was less than 85 percent of the predicted value for age was twice that among women whose exercise capacity was at least 85 percent of the age-predicted value (P<0.001). Results were similar in the cohort of symptomatic women. CONCLUSIONS: We have established a nomogram for predicted exercise capacity on the basis of age that is predictive of survival among both asymptomatic and symptomatic women. These findings could be incorporated into the interpretation of exercise stress tests, providing additional prognostic information for risk stratification.

Solvability of singular second order m-point boundary value problems of Dirichlet type

Let f : [0, 1] x R2 -> R be a function satisfying the Caxatheodory conditions and t(1 - t)e(t) epsilon L-1 (0, 1). Let a(i) epsilon R and xi(i) (0, 1) for i = 1,..., m - 2 where 0 < xi(1) < xi(2) < (...) < xi(m-2) < 1 - In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem [GRAPHICS] The proof of our main result is based on the Leray-Schauder continuation theorem.

Regression to the mean: what it is and how to deal with it

Background Regression to the mean (RTM) is a statistical phenomenon that can make natural variation in repeated data look like real change. It happens when unusually large or small measurements tend to be followed by measurements that are closer to the mean. Methods We give some examples of the phenomenon, and discuss methods to overcome it at the design and analysis stages of a study. Results The effect of RTM in a sample becomes more noticeable with increasing measurement error and when follow-up measurements are only examined on a sub-sample selected using a baseline value. Conclusions RTM is a ubiquitous phenomenon in repeated data and should always be considered as a possible cause of an observed change. Its effect can be alleviated through better study design and use of suitable statistical methods.

Using extreme value theory to measure value-at-risk for daily electricity spot prices

The recent deregulation in electricity markets worldwide has heightened the importance of risk management in energy markets. Assessing Value-at-Risk (VaR) in electricity markets is arguably more difficult than in traditional financial markets because the distinctive features of the former result in a highly unusual distribution of returns-electricity returns are highly volatile, display seasonalities in both their mean and volatility, exhibit leverage effects and clustering in volatility, and feature extreme levels of skewness and kurtosis. With electricity applications in mind, this paper proposes a model that accommodates autoregression and weekly seasonals in both the conditional mean and conditional volatility of returns, as well as leverage effects via an EGARCH specification. In addition, extreme value theory (EVT) is adopted to explicitly model the tails of the return distribution. Compared to a number of other parametric models and simple historical simulation based approaches, the proposed EVT-based model performs well in forecasting out-of-sample VaR. In addition, statistical tests show that the proposed model provides appropriate interval coverage in both unconditional and, more importantly, conditional contexts. Overall, the results are encouraging in suggesting that the proposed EVT-based model is a useful technique in forecasting VaR in electricity markets. (c) 2005 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

Advanced mean field methods:theory and practice

A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

What do public values mean for public action? Putting public values in their plural place

Public values are moving from a research concern to policy discourse and management practice. There are, though, different readings of what public values actually mean. Reflection suggests two distinct strands of thinking: a generative strand that sees public value emerging from processes of public debate; and an institutional interpretation that views public values as the attributes of government producers. Neither perspective seems to offer a persuasive account of how the public gains from strengthened public values. Key propositions on values are generated from comparison of influential texts. A provisional framework is presented of the values base of public institutions and the loosely coupled public propositions flowing from these values. Value propositions issue from different governing contexts, which are grouped into policy frames that then compete with other problem frames for citizens’ cognitive resources. Vital democratic commitments to pluralism require public values to be distributed in competition with other, respected, frames.

A probabilistic indirect adaptive control for systems with input-dependent noise

A probabilistic indirect adaptive controller is proposed for the general nonlinear multivariate class of discrete time system. The proposed probabilistic framework incorporates input–dependent noise prediction parameters in the derivation of the optimal control law. Moreover, because noise can be nonstationary in practice, the proposed adaptive control algorithm provides an elegant method for estimating and tracking the noise. For illustration purposes, the developed method is applied to the affine class of nonlinear multivariate discrete time systems and the desired result is obtained: the optimal control law is determined by solving a cubic equation and the distribution of the tracking error is shown to be Gaussian with zero mean. The efficiency of the proposed scheme is demonstrated numerically through the simulation of an affine nonlinear system.

Fully probabilistic control design in an adaptive critic framework

Optimal stochastic controller pushes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design (FPD) uses probabilistic description of the desired closed loop and minimizes Kullback-Leibler divergence of the closed-loop description to the desired one. Practical exploitation of the fully probabilistic design control theory continues to be hindered by the computational complexities involved in numerically solving the associated stochastic dynamic programming problem. In particular very hard multivariate integration and an approximate interpolation of the involved multivariate functions. This paper proposes a new fully probabilistic contro algorithm that uses the adaptive critic methods to circumvent the need for explicitly evaluating the optimal value function, thereby dramatically reducing computational requirements. This is a main contribution of this short paper.

The Value of Knowing that You Do Not Know

The value of knowing about data availability and system accessibility is analyzed through theoretical models of Information Economics. When a user places an inquiry for information, it is important for the user to learn whether the system is not accessible or the data is not available, rather than not have any response. In reality, various outcomes can be provided by the system: nothing will be displayed to the user (e.g., a traffic light that does not operate, a browser that keeps browsing, a telephone that does not answer); a random noise will be displayed (e.g., a traffic light that displays random signals, a browser that provides disorderly results, an automatic voice message that does not clarify the situation); a special signal indicating that the system is not operating (e.g., a blinking amber indicating that the traffic light is down, a browser responding that the site is unavailable, a voice message regretting to tell that the service is not available). This article develops a model to assess the value of the information for the user in such situations by employing the information structure model prevailing in Information Economics. Examples related to data accessibility in centralized and in distributed systems are provided for illustration.

On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball

2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05

Anti-Periodic Boundary Value Problem for Impulsive Fractional Integro Differential Equations

MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37

A randomised controlled trial of the clinical effectiveness and cost-effectiveness of the levonorgestrel-releasing intrauterine system in primary care against standard treatment for menorrhagia:the ECLIPSE trial

BACKGROUND: Heavy menstrual bleeding (HMB) is a common problem, yet evidence to inform decisions about initial medical treatment is limited. OBJECTIVES: To assess the clinical effectiveness and cost-effectiveness of the levonorgestrel-releasing intrauterine system (LNG-IUS) (Mirena(®), Bayer) compared with usual medical treatment, with exploration of women's perspectives on treatment. DESIGN: A pragmatic, multicentre randomised trial with an economic evaluation and a longitudinal qualitative study. SETTING: Women who presented in primary care. PARTICIPANTS: A total of 571 women with HMB. A purposeful sample of 27 women who were randomised or ineligible owing to treatment preference participated in semistructured face-to-face interviews around 2 and 12 months after commencing treatment. INTERVENTIONS: LNG-IUS or usual medical treatment (tranexamic acid, mefenamic acid, combined oestrogen-progestogen or progesterone alone). Women could subsequently swap or cease their allocated treatment. OUTCOME MEASURES: The primary outcome was the patient-reported score on the Menorrhagia Multi-Attribute Scale (MMAS) assessed over a 2-year period and then again at 5 years. Secondary outcomes included general quality of life (QoL), sexual activity, surgical intervention and safety. Data were analysed using iterative constant comparison. A state transition model-based cost-utility analysis was undertaken alongside the randomised trial. Quality-adjusted life-years (QALYs) were derived from the European Quality of Life-5 Dimensions (EQ-5D) and the Short Form questionnaire-6 Dimensions (SF-6D). The intention-to-treat analyses were reported as cost per QALY gained. Uncertainty was explored by conducting both deterministic and probabilistic sensitivity analyses. RESULTS: The MMAS total scores improved significantly in both groups at all time points, but were significantly greater for the LNG-IUS than for usual treatment [mean difference over 2 years was 13.4 points, 95% confidence interval (CI) 9.9 to 16.9 points; p < 0.001]. However, this difference between groups was reduced and no longer significant by 5 years (mean difference in scores 3.9 points, 95% CI -0.6 to 8.3 points; p = 0.09). By 5 years, only 47% of women had a LNG-IUS in place and 15% were still taking usual medical treatment. Five-year surgery rates were low, at 20%, and were similar, irrespective of initial treatments. There were no significant differences in serious adverse events between groups. Using the EQ-5D, at 2 years, the relative cost-effectiveness of the LNG-IUS compared with usual medical treatment was £1600 per QALY, which by 5 years was reduced to £114 per QALY. Using the SF-6D, usual medical treatment dominates the LNG-IUS. The qualitative findings show that women's experiences and expectations of medical treatments for HMB vary considerably and change over time. Women had high expectations of a prompt effect from medical treatments. CONCLUSIONS: The LNG-IUS, compared with usual medical therapies, resulted in greater improvement over 2 years in women's assessments of the effect of HMB on their daily routine, including work, social and family life, and psychological and physical well-being. At 5 years, the differences were no longer significant. A similar low proportion of women required surgical intervention in both groups. The LNG-IUS is cost-effective in both the short and medium term, using the method generally recommended by the National Institute for Health and Care Excellence. Using the alternative measures to value QoL will have a considerable impact on cost-effectiveness decisions. It will be important to explore the clinical and health-care trajectories of the ECLIPSE (clinical effectiveness and cost-effectiveness of levonorgestrel-releasing intrauterine system in primary care against standard treatment for menorrhagia) trial participants to 10 years, by which time half of the cohort will have reached menopause. TRIAL REGISTRATION: Current Controlled Trials ISRCTN86566246. FUNDING: This project was funded by the NIHR Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 19, No. 88. See the NIHR Journals Library website for further project information.

A probabilistic approach to the estimation of regional photovoltaic power generation using meteorological data

In Germany the upscaling algorithm is currently the standard approach for evaluating the PV power produced in a region. This method involves spatially interpolating the normalized power of a set of reference PV plants to estimate the power production by another set of unknown plants. As little information on the performances of this method could be found in the literature, the first goal of this thesis is to conduct an analysis of the uncertainty associated to this method. It was found that this method can lead to large errors when the set of reference plants has different characteristics or weather conditions than the set of unknown plants and when the set of reference plants is small. Based on these preliminary findings, an alternative method is proposed for calculating the aggregate power production of a set of PV plants. A probabilistic approach has been chosen by which a power production is calculated at each PV plant from corresponding weather data. The probabilistic approach consists of evaluating the power for each frequently occurring value of the parameters and estimating the most probable value by averaging these power values weighted by their frequency of occurrence. Most frequent parameter sets (e.g. module azimuth and tilt angle) and their frequency of occurrence have been assessed on the basis of a statistical analysis of parameters of approx. 35 000 PV plants. It has been found that the plant parameters are statistically dependent on the size and location of the PV plants. Accordingly, separate statistical values have been assessed for 14 classes of nominal capacity and 95 regions in Germany (two-digit zip-code areas). The performances of the upscaling and probabilistic approaches have been compared on the basis of 15 min power measurements from 715 PV plants provided by the German distribution system operator LEW Verteilnetz. It was found that the error of the probabilistic method is smaller than that of the upscaling method when the number of reference plants is sufficiently large (>100 reference plants in the case study considered in this chapter). When the number of reference plants is limited (<50 reference plants for the considered case study), it was found that the proposed approach provides a noticeable gain in accuracy with respect to the upscaling method.

Cornered Asymptotically Hyperbolic Metrics

Thesis (Ph.D.)--University of Washington, 2016-08