Optimal offering strategies for wind power producers considering uncertainty and risk

This paper provides a two-stage stochastic programming approach for the development of optimal offering strategies for wind power producers. Uncertainty is related to electricity market prices and wind power production. A hybrid intelligent approach, combining wavelet transform, particle swarm optimization and adaptive-network-based fuzzy inference system, is used in this paper to generate plausible scenarios. Also, risk aversion is explicitly modeled using the conditional value-at-risk methodology. Results from a realistic case study, based on a wind farm in Portugal, are provided and analyzed. Finally, conclusions are duly drawn.

Scheduling of a hydro producer considering head-dependency, price scenarios and risk-aversion

In this paper, a mixed-integer quadratic programming approach is proposed for the short-term hydro scheduling problem, considering head-dependency, discontinuous operating regions and discharge ramping constraints. As new contributions to earlier studies, market uncertainty is introduced in the model via price scenarios, and risk aversion is also incorporated by limiting the volatility of the expected profit through the conditional value-at-risk. Our approach has been applied successfully to solve a case Study based on one of the main Portuguese cascaded hydro systems, requiring a negligible computational time.

Projecto solvência II - Modelação do risco de subscrição numa companhia de seguros não vida

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Matemática e Aplicações - Actuariado, Estatística e Investigação Operacional

Toxoplasma-IgM and IgG-avidity in single samples from areas with a high infection rate can determine the risk of mother-to-child transmission

Anti-Toxoplasma IgG-avidity was determined in 168 serum samples from IgG- and IgM-positive pregnant women at various times during pregnancy, in order to evaluate the predictive value for risk of mother-to-child transmission in a single sample, taking the limitations of conventional serology into account. The neonatal IgM was considered the serologic marker of transmission. Fluorometric tests for IgG, IgM (immunocapture) and IgG-avidity were performed. Fifty-one of the 128 pregnant women tested gave birth in the hospital and neonatal IgM was obtained. The results showed 32 (62.75%) pregnant women having high avidity, IgM indexes between 0.6 and 2.4, and no infected newborn. Nineteen (37.25%) had low or inconclusive avidity, IgM indexes between 0.6 and 11.9, and five infected newborns and one stillbirth. In two infected newborns and the stillbirth maternal IgM indexes were low and in one infected newborn the only maternal parameter that suggested fetal risk was IgG-avidity. In the present study, IgG-avidity performed in single samples from positive IgM pregnant women helped to determine the risk of transmission at any time during pregnancy, especially when the indexes of the two tests were analysed with respect to gestational age. This model may be less expensive in developing countries where there is a high prevalence of infection than the follow-up of susceptible mothers until childbirth with monthly serology, and it creates a new perspective for the diagnosis of congenital toxoplasmosis.

Risco Operacional nas seguradoras – Estudo do caso Generali

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação

Haar wavelets-based approach for quantifying credit portfolio losses

This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelet basis functions and calculate the coefficients of the approximation by inverting its Laplace transform. The Wavelet Approximation (WA) method is specially suitable for non-smooth distributions, often arising in small or concentrated portfolios, when the hypothesis of the Basel II formulas are violated. To test the methodology we consider the Vasicek one-factor portfolio credit loss model as our model framework. WA is an accurate, robust and fast method, allowing to estimate VaR much more quickly than with a Monte Carlo (MC) method at the same level of accuracy and reliability.

Solvency Capital estimation and Risk Measures

This paper examines why a financial entity’s solvency capital estimation might be underestimated if the total amount required is obtained directly from a risk measurement. Using Monte Carlo simulation we show that, in some instances, a common risk measure such as Value-at-Risk is not subadditive when certain dependence structures are considered. Higher risk evaluations are obtained for independence between random variables than those obtained in the case of comonotonicity. The paper stresses, therefore, the relationship between dependence structures and capital estimation.

Extremal properties of certain risk models

Cette thèse s'intéresse à étudier les propriétés extrémales de certains modèles de risque d'intérêt dans diverses applications de l'assurance, de la finance et des statistiques. Cette thèse se développe selon deux axes principaux, à savoir: Dans la première partie, nous nous concentrons sur deux modèles de risques univariés, c'est-à- dire, un modèle de risque de déflation et un modèle de risque de réassurance. Nous étudions le développement des queues de distribution sous certaines conditions des risques commun¬s. Les principaux résultats sont ainsi illustrés par des exemples typiques et des simulations numériques. Enfin, les résultats sont appliqués aux domaines des assurances, par exemple, les approximations de Value-at-Risk, d'espérance conditionnelle unilatérale etc. La deuxième partie de cette thèse est consacrée à trois modèles à deux variables: Le premier modèle concerne la censure à deux variables des événements extrême. Pour ce modèle, nous proposons tout d'abord une classe d'estimateurs pour les coefficients de dépendance et la probabilité des queues de distributions. Ces estimateurs sont flexibles en raison d'un paramètre de réglage. Leurs distributions asymptotiques sont obtenues sous certaines condi¬tions lentes bivariées de second ordre. Ensuite, nous donnons quelques exemples et présentons une petite étude de simulations de Monte Carlo, suivie par une application sur un ensemble de données réelles d'assurance. L'objectif de notre deuxième modèle de risque à deux variables est l'étude de coefficients de dépendance des queues de distributions obliques et asymétriques à deux variables. Ces distri¬butions obliques et asymétriques sont largement utiles dans les applications statistiques. Elles sont générées principalement par le mélange moyenne-variance de lois normales et le mélange de lois normales asymétriques d'échelles, qui distinguent la structure de dépendance de queue comme indiqué par nos principaux résultats. Le troisième modèle de risque à deux variables concerne le rapprochement des maxima de séries triangulaires elliptiques obliques. Les résultats théoriques sont fondés sur certaines hypothèses concernant le périmètre aléatoire sous-jacent des queues de distributions. -- This thesis aims to investigate the extremal properties of certain risk models of interest in vari¬ous applications from insurance, finance and statistics. This thesis develops along two principal lines, namely: In the first part, we focus on two univariate risk models, i.e., deflated risk and reinsurance risk models. Therein we investigate their tail expansions under certain tail conditions of the common risks. Our main results are illustrated by some typical examples and numerical simu¬lations as well. Finally, the findings are formulated into some applications in insurance fields, for instance, the approximations of Value-at-Risk, conditional tail expectations etc. The second part of this thesis is devoted to the following three bivariate models: The first model is concerned with bivariate censoring of extreme events. For this model, we first propose a class of estimators for both tail dependence coefficient and tail probability. These estimators are flexible due to a tuning parameter and their asymptotic distributions are obtained under some second order bivariate slowly varying conditions of the model. Then, we give some examples and present a small Monte Carlo simulation study followed by an application on a real-data set from insurance. The objective of our second bivariate risk model is the investigation of tail dependence coefficient of bivariate skew slash distributions. Such skew slash distributions are extensively useful in statistical applications and they are generated mainly by normal mean-variance mixture and scaled skew-normal mixture, which distinguish the tail dependence structure as shown by our principle results. The third bivariate risk model is concerned with the approximation of the component-wise maxima of skew elliptical triangular arrays. The theoretical results are based on certain tail assumptions on the underlying random radius.

Incremental Prognostic Value of Myocardial Blood Flow Quantification with Rb-82 Cardiac PET in Patients With Known or Suspected CAD

Rb-82cardiac PET has been used to non-invasively assess myocardial blood flow (MBF)and myocardial flow reserve (MFR). The impact of MBF and MFR for predictingmajor adverse cardiovascular events (MACE) has not been investigated in aprospective study, which was our aim. MATERIAL AND METHODS: In total, 280patients (65±10y, 36% women) with known or suspected CAD were prospectivelyenrolled. They all underwent both a rest and adenosine stress Rb-82 cardiacPET/CT. Dynamic acquisitions were processed with the FlowQuant 2.1.3 softwareand analyzed semi-quantitatively (SSS, SDS) and quantitatively (MBF, MFR) andreported using the 17-segment AHA model. Patients were stratified based on SDS,stress MBF and MFR and allocated into tertiles. For each group, annualizedevent rates were computed by dividing the number of annualized MACE (cardiacdeath, myocardial infarction, revascularisation or hospitalisation forcardiac-related event) by the sum of individual follow-up periods in years.Outcome were analysed for each group using Kaplan-Meier event-free survivalcurves and compared using the log-rank test. Multivariate analysis wasperformed in a stepwise fashion using Cox proportional hazards regressionmodels (p<0.05 for model inclusion). RESULTS: In a median follow-up of 256days (range 168-440d), 44 MACE were observed. Ischemia (SDS≥2) was observed in95 patients who had higher annualized MACE rate as compared to those without(55% vs. 9.8%, p<0.0001). The group with the lowest MFR tertile (MFR<1.76)had higher MACE rate than the two highest tertiles (51% vs. 9% and 14%,p<0.0001). Similarly, the group with the lowest stress MBF tertile(MBF<1.78mL/min/g) had the highest annualized MACE rate (41% vs. 26% and 6%,p=0.0002). On multivariate analysis, the addition of MFR or stress MBF to SDSsignificantly increased the global χ2 (from 56 to 60, p=0.04; and from56 to 63, p=0.01). The best prognostic power was obtained in a model combiningSDS (p<0.001) and stress MBF (p=0.01). Interestingly, the integration ofstress MBF enhanced risk stratification even in absence of ischemia.CONCLUSIONS: Quantification of MBF or MFR in Rb-82 cardiac PET/CT providesindependent and incremental prognostic information over semi-quantitativeassessment with SDS and is of value for risk stratification.

Buy-and-Hold Strategies and Comonotonic Approximations

[cat] En aquest article estudiem estratègies “comprar i mantenir” per a problemes d’optimitzar la riquesa final en un context multi-període. Com que la riquesa final és una suma de variables aleatòries dependents, on cadascuna d’aquestes correspon a una quantitat de capital que s’ha invertit en un actiu particular en una data determinada, en primer lloc considerem aproximacions que redueixen l’aleatorietat multivariant al cas univariant. A continuació, aquestes aproximacions es fan servir per determinar les estratègies “comprar i mantenir” que optimitzen, per a un nivell de probabilitat donat, el VaR i el CLTE de la funció de distribució de la riquesa final. Aquest article complementa el treball de Dhaene et al. (2005), on es van considerar estratègies de reequilibri constant.

Buy-and-Hold Strategies and Comonotonic Approximations

[cat] En aquest article estudiem estratègies “comprar i mantenir” per a problemes d’optimitzar la riquesa final en un context multi-període. Com que la riquesa final és una suma de variables aleatòries dependents, on cadascuna d’aquestes correspon a una quantitat de capital que s’ha invertit en un actiu particular en una data determinada, en primer lloc considerem aproximacions que redueixen l’aleatorietat multivariant al cas univariant. A continuació, aquestes aproximacions es fan servir per determinar les estratègies “comprar i mantenir” que optimitzen, per a un nivell de probabilitat donat, el VaR i el CLTE de la funció de distribució de la riquesa final. Aquest article complementa el treball de Dhaene et al. (2005), on es van considerar estratègies de reequilibri constant.

An application of capital allocation principles to operational risk

The cost of operational risk refers to the capital needed to a fford the loss generated by ordinary activities of a firm. In this work we demonstrate how allocation principles can be used to the subdivision of the aggregate capital so that the firm can distribute this cost across its various constituents that generate operational risk. Several capital allocation principles are revised. Proportional allocation allows to calculate a relative risk premium to be charged to each unit. An example of fraud risk in the banking sector is presented and some correlation scenarios between business lines are compared. Keywords: solvency, quantile, value at risk, copulas

INCLUDING RISK IN ECONOMIC FEASIBILITY ANALYSIS:A STOCHASTIC SIMULATION MODEL FOR BLUEBERRY INVESTMENT DECISIONS IN CHILE

ABSTRACT The traditional method of net present value (NPV) to analyze the economic profitability of an investment (based on a deterministic approach) does not adequately represent the implicit risk associated with different but correlated input variables. Using a stochastic simulation approach for evaluating the profitability of blueberry (Vaccinium corymbosum L.) production in Chile, the objective of this study is to illustrate the complexity of including risk in economic feasibility analysis when the project is subject to several but correlated risks. The results of the simulation analysis suggest that the non-inclusion of the intratemporal correlation between input variables underestimate the risk associated with investment decisions. The methodological contribution of this study illustrates the complexity of the interrelationships between uncertain variables and their impact on the convenience of carrying out this type of business in Chile. The steps for the analysis of economic viability were: First, adjusted probability distributions for stochastic input variables (SIV) were simulated and validated. Second, the random values of SIV were used to calculate random values of variables such as production, revenues, costs, depreciation, taxes and net cash flows. Third, the complete stochastic model was simulated with 10,000 iterations using random values for SIV. This result gave information to estimate the probability distributions of the stochastic output variables (SOV) such as the net present value, internal rate of return, value at risk, average cost of production, contribution margin and return on capital. Fourth, the complete stochastic model simulation results were used to analyze alternative scenarios and provide the results to decision makers in the form of probabilities, probability distributions, and for the SOV probabilistic forecasts. The main conclusion shown that this project is a profitable alternative investment in fruit trees in Chile.

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.

Korkoriskin mittaaminen ja hallinta: Case Etelä-Karjalan Osuuspankki

Tutkielman päätavoitteena on eri menetelmillä selvittää Etelä-Karjalan Osuuspankin korkoriskin suuruus sekä luoda Etelä-Karjalan Osuuspankille suojausstrategia. Alatavoitteena on tarkastella, että miten pankki on tähän mennessä havainnut korkoriskin ja miten sitä vastaan on suojauduttu. Korkoriskiä tutkielmassa tullaan mittaamaan gap-, duraatio- sekä VaR-analyyseillä. Tutkielman alussa on perehdytty teoriapohjalta korkoriskin muodostumiseen, mittaamiseen sekä korkoriskiltä suojautumiseen. Teoriaosuuden havaintoja on hyödynnetty myöhemmin tutkielman empiirisessä osassa. Etelä-Karjalan Osuuspankin suurin ongelma korkoriskin näkökulmasta on se, että suuri osa tulevista korkotuotoista on vaihtuvakorkoisia, kun taas suuri osa tulevaisuuden korkokuluista on kiinteäkorkoisia. Suojausstrategia luodaan juuri tälle epäkohdalle.