[pt] A contratação de energia elétrica no Brasil por parte de grandes consumidores é feita de acordo com o nível de tensão e considerando dois ambientes: o Ambiente Regulado e o Ambiente Livre. Os grandes consumidores são aqueles que possuem carga igual ou superior a 3 MW, atendidos em qualquer nível de tensão e a energia pode ser contratada em quaisquer desses ambientes. Um grande desafio para esses consumidores é determinar a melhor alternativa de contratação. Para tratar este problema, é preciso ter em conta que o consumo de energia e a demanda de potência requerida são variáveis desconhecidas no momento da contratação do consumidor, sendo necessário estimá-las. Esta dissertação propõe atacar este problema por uma metodologia que envolve simulação de cenários futuros de demanda máxima de potência e energia total consumida e otimização estocástica dos cenários simulados para definir o melhor contrato. Dada a natureza estocástica do problema, empregou-se o CVaR (Conditional Value at Risk) como medida de risco para o problema de otimização. Para ilustrar, os resultados da contratação foram obtidos para um grande consumidor real considerando a modalidade Verde A4 no Ambiente Regulado e um contrato de quantidade no Ambiente Livre. / [en] The energy contracting in Brazil for large consumers is done according to the voltage level and considering two environments: the Regulated Environment and the Free Environment. Large consumers are those characterized by installed load equal to or greater than 3 MW, supplied at any voltage level and its energy contract can be chosen between any of these two environments. A major challenge for these consumers is to determine the best alternative of contracting. To address this problem, it must be taken into account that the energy consumption and the required power demand are unknown variables by the time of consumer contracting, being necessary to estimate them. This dissertation proposes to tackle this problem by a methodology based on the simulation of future scenarios of maximum power demand and total consumed energy and on stochastic optimization of these simulated scenarios in order to define the best contract. Given the stochastic nature of the problem, it was used the CVaR (Conditional Value at Risk) as a measure of risk for the optimization problem. To illustrate, the contracting results were obtained for a large real consumer considering the Green Tariff group A4 in the Regulated Environment and a quantity contract in the Free Environment.

För investerare vars portföljer utgörs av internationella investeringar är det i synnerhet viktigt att begrunda beroendestrukturen mellan internationella investeringar och valutakurser. Detta på grund av den valutarisk som investeraren exponerar sig mot utöver de internationella tillgångarnas inneboende risk. I denna studie undersöks hur svenska investerare med investeringar i den amerikanska aktie- och företagsobligationsmarknaden påverkas av valutakursförändringar i USD:SEK. De amerikanska investeringarna är i denna studie denominerade i amerikanska dollar men portföljen och dess risk är denominerad i svenska kronor, portföljen påverkas därmed av valutaeffekten.Vidare undersöks samvariationen mellan dessa tillgångar och en optimal valutahedge upprättas för att reducera svansrisk i en sådan portfölj.  För att bestämma en optimal valutahedge optimeras CVaR för nio olika portföljer med olika viktning av S&P 500, investment grade- företagsobligationer och high yield-företagsobligationer. Två metoder för att ta fram scenariopriser till optimeringen används: historisk simulering samt Monte Carlo-simulering från en vine-copula. Resultaten i denna studie antyder att svenska investerare bör hedga bort viss exponering mot USD. På den amerikanska aktiemarknaden bör större andel av valutarisken bibehållas än på den amerikanska high yield-obligationsmarknaden. Detta antyder att viss valutarisk bidrar med en hedgande effekt. På den amerikanska investment grade-obligationsmarknaden bör endast en mycket liten exponering mot USD bibehållas och ingen tydlig hedgande effekt kunde påvisas. Analys av samvariation mellan amerikansk aktiemarknad, företagsobligationsmarknad och valutakursen USD:SEK antyder att USD:SEK uppvisar förhöjt negativt beroende vid svansutfall i både den amerikanska aktiemarknaden och high yield-obligationsmarknaden. Detta antyder att USD uppvisar så kallade safe haven-egenskaper för svenska investerare i dessa marknader. / For investors whose portfolios consist of international investments, it is of particular importance to consider the dependence structure between international investments and foreign exchange rates. This is due to the currency risk that the investor is exposed to in addition to the inherent risk of the international assets. This study examines how Swedish investors with investments in the US equity and corporate bond market are affected by exchange rate fluctuations in the currency pair USD:SEK. In this study, US investments are denominated in US dollars, but the portfolio and its risk are denominated in Swedish Kronor, the portfolio is thus affected by the foreign currency effect. Furthermore, the covariation between these assets is examined and an optimal hedge is established in order to reduce tail risk in such a portfolio. To determine the optimal currency hedge, CVaR is optimized for nine different portfolios with different weightings of S&P 500, investment grade corporate bonds and high yield corporate bonds. Two methods for producing scenario prices for the optimization are used: historical simulation and Monte Carlo simulation from a vine copula. The results of this study suggest that Swedish investors should hedge some of the exposure against USD. In the US stock market, a larger share of currency risk should be maintained than in the US high yield bond market. This suggests that some currency risk contributes to a hedging effect. In the US investment grade bond market little exposure against USD should be maintained and no clear hedging effect could be demonstrated. Analysis of covariation between the US stock market, corporate bond market and the exchange rate USD:SEK indicates that USD:SEK displays increased negative dependence in tail events in boththe US stock market and the high yield bond market. This indicates that USD displays so-called safe haven properties for Swedish investors in these markets.

In this thesis, a portfolio optimization with integer variables which influ- ence optimal assets allocation, is studied. Measures of risk are defined and the cor- responding mean-risk models are derived. Two methods are used to develop robust models involving uncertainty in probability distribution: the worst-case analyses and contamination. The uncertainty in values of scenarios and in their probabili- ties of the discrete probability distribution is assumed separately followed by their combination. These models are applied to stock market data with using optimization software GAMS.

In this thesis, a portfolio optimization with integer variables which influence optimal assets allocation in domestic as well as in international environment, is studied. At the beginning with basic terms, assets and portfolio background, incentives of portfolio creation, fields of portfolio application and portfolio management is dealt. Following the characteristics of assets and portfolios (expected return, risk, liquidity), which are used by investors to value their properties, are introduced. Next the mean-risk models are derived for the measures of risk - variance, Value at Risk, Conditional Value at Risk and prepared for a practical application. Heuristics implemented in Matlab and standard algorithms of software GAMS are used for solving problems of the portfolio optimization. At the end optimization methods are applied on real financial data and an outputs are compared.

Moment Problems with Applications to Value-At-Risk and Portfolio Management By Ruilin Tian May 2008 Committee Chair: Dr. Samuel H. Cox Major Department: Risk Management and Insurance My dissertation provides new applications of moment theory and optimization to financial and insurance risk management. In the investment and managerial areas, one often needs to determine some measure of risk, especially the risk of extreme events. However, complete information of the underlying outcomes is usually unavailable; instead one has access to partial information such as the mean, variance, mode, or range. In Chapters 2 and 3, we find the semiparametric upper and lower bounds for the value-at-risk (VaR) with incomplete information, that is, moments of the underlying distribution. When a single variable is concerned, bounds on VaR are computed to obtain a 100% confidence interval. When the sample financial data have a global maximum, we show that unimodal assumption tightens the optimal bounds. Next we further analyze a function of two correlated random variables. Specifically, we find bounds on the probability of two joint extreme events. When three or more variables are involved, the multivariate problem can sometimes be converted to a single variable problem. In all cases, we use the physical measure rather than the commonly used equivalent pricing probability measure. In addition to solving these problems using the traditional approach based on the geometry of a moment problem, a more efficient method is proposed to solve a general class of moment bounds via semidefinite programming. In the last part of the thesis, we apply optimization techniques to improve financial portfolio risk management. Instead of considering VaR, we work with a coherent risk measure, the conditional VaR (CVaR). As an extension of Krokhmal et al. (2002), we impose CVaR-related functions to the portfolio selection problem. The CVaR approach sets a β-level CVaR as the objective function and maximizes the worst case on the tail of the distribution. The CVaR-like constraints approach adds a set of CVaR-like constraints to the traditional Markowitz problem, reshaping the portfolio distribution. Both methods greatly increase the skewness of portfolios, although the CVaR approach may lose control of the variance. This capability of increasing skewness is very attractive to the investors who may prefer higher probability of obtaining higher returns. We compare the CVaR-related approaches to some other popular portfolio optimization methods. Our numerical analysis provides empirical support for the superiority of the CVaR-like constraints approach in terms of portfolio efficiency.

外匯資產組合的主要風險通常來自於：貨幣風險、市場風險、信用風險、流動性風險以及操作風險。貨幣風險指的是因為匯率波動所造成的資本市場損失。VaR是最常被用來衡量此種風險的指標。然而，由於VaR的某些特性，使得它在用來衡量資產組合風險時有許多限制。 CVaR則是一較佳的衡量指標。它的好處在於它符合數學的性質。在本文中，我們利用兩階段求解的概念，這使得我們可輕易的將CVaR的概念作更多的延伸。我們導入ICC的概念來計算CVaR，這讓CVaR更為直覺，也因此更易使用。因此，只要確認損失來源，並將隨機變數帶入損失方程式，即可知道該資產組合所需承擔的風險。 最後，我們利用這個模型，從央行的角度來討論台灣的外匯市場。我們利用CVaRMin來進行討論並歸納一些結論以供後續研究使用。 / The main risk of a foreign asset portfolio usually comes from: currency risk, market risk, credit risk, liquidity risk, and operation risk. Currency risk is the risk of capital market losses as a consequence of fluctuations in exchange rate. VaR is the most frequently used concept for measuring market risk and recently is applied to currency risk. However VaR is somewhat restricted when it is used to measure the risk of a portfolio management. CVaR is an alternative. The superiority of CVaR lies in its accordance to mathematical properties. In this study, we apply the concept of two-stage recourse model intuition in management of risk and then easily extend the approach of CVaR. We introduce the ICC. This makes CVaR more straightforward. As long as one can identify the source of losses and substitute the random factors into shortage function, he can easily know the risk he will take. Finally we discuss Taiwan foreign exchange management from a view point of the Central Bank. We conduct this experiment by a solver called CVaRMin and summarize some points for further researches.

The Fourth Swedish National Pension Fund (AP4), as well as many other large investors, has noted deficiencies the Mean-Variance framework for portfolio management of asset with non-normal characteristics. The main problem apparent in the Mean-Variance framework, when investing in alternative assets such as hedge funds, is the lacking systematic control of the balance between the measurements of risk due normal variation and tail-risk. Hedge funds constitute an asset class distinguished by non-normal characteristics such as negative skewness and heavy excess kurtosis, which suggests normality should not be assumed when optimizing a portfolio of hedge funds. Certain hedge fund strategies aim to be uncorrelated to other hedge funds and the major asset markets and are thus expected to have the capacity to hedge against extreme market events. Hedge fund performance during historically volatile market periods, including heavy losses and liquidations, has however proved this untrue. Outcomes in the tail of hedge fund distributions rather appear to occur in conjunction with increased correlation toward external indicators such as the equity stock market. With the aim to consider tail events in a portfolio of hedge funds and index futures, an optimization model intending to capture the asymmetric covariance between hedge fund assets and the equity market is developed and evaluated. The theory of copulas is applied to estimate the multivariate distribution by separating assumptions regarding univariate characteristics and dependence between assets. The estimated multivariate distribution is thereafter utilized in a scenario-based optimization model applying the Conditional Value at Risk (CVaR) measure as a risk measure, to capture events in the left tail of the portfolio distribution. The proposed GARCH-C-Vine-Mean-CVaR model is presented and evaluated against two reference models, a GARCH-C-Vine-Mean-Variance model, and a model assuming a multivariate normal distribution, EWMA-Mean-Variance. The ability to capture realized outcomes is analyzed for all three models, where the proposed GARCH-C-Vine-Mean-CVaR as well as the GARCH-C-Vine-Mean-Variance model show to capture realized outcomes to a further extent than the model assuming a multivariate normal distribution. Further, applying the risk measure CVaR has in this study shown to capture the realized outcomes to the same extent as applying variance as the risk measure. In conclusion, the proposed model manages to capture tail-events in the data analyzed in this study, to a further extent than if assuming multivariate normality. The lack of regulations and bias that denote hedge fund reporting, does however prevent a conclusion on whether the proposed model captures actual realized tail-events of hedge fund returns.

No description available.

A growing need for clean and sustainable energy is causing a significant shift in the electricity generation paradigm. In the electricity system of the future, integration of renewable energy sources with smart grid technologies can lead to potentially huge economical and environmental benefits ranging from lesser dependency on fossil fuels and improved efficiency to greater reliability and eventually reduced cost of electricity. In this context, microgrids serve as one of the main components of smart grids with high penetration of renewable resources and modern control strategies. This dissertation is concerned with developing optimal control strategies to manage an energy storage unit in a grid-connected microgrid under uncertainty of electricity demand and prices. Two methods are proposed based on the concept of rolling horizon control, where charge/discharge activities of the storage unit are determined by repeatedly solving an optimization problem over a moving control window. The predicted values of the microgrid net electricity demand and electricity prices over the control horizon are assumed uncertain. The first formulation of the control is based on the scenario-based stochastic conditional value at risk (CVaR) optimization, where the cost function includes electricity usage cost, battery operation costs, and grid signal smoothing objectives. Gaussian uncertainty is assumed in both net demand and electricity prices. The second formulation reduces the computations by taking a worst-case CVaR stochastic optimization approach. In this case, the uncertainty in demand is still stochastic but the problem constraints are made robust with respect to price changes in a given range. The optimization problems are initially formulated as mixed integer linear programs (MILP), which are non-convex. Later, reformulations of the optimization problems into convex linear programs are presented, which are easier and faster to solve. Simulation results under different operation scenarios are presented to demonstrate the effectiveness of the proposed methods. Finally, the energy management problem in network of grid-connected microgrids is investigated and a strategy is devised to allocate the resulting net savings/costs of operation of the microgrids to the individual microgrids. In the proposed approach, the energy management problem is formulated in a deterministic co-operative game theoretic framework for a group of connected microgrids as a single entity and the individual savings are distributed based on the Shapley value theory. Simulation results demonstrate that this co-operation leads to higher economical return for individual microgrids compared to the case where each of them is operating independently. Furthermore, this reduces the dependency of the microgrids on the utility grid by exchanging power locally. / Thesis / Master of Applied Science (MASc)

[pt] No seu planejamento plurianual de investimentos, as organizações do setor de Exploração e Produção (EeP) estruturam alternativas de projetos de produção de petróleo e gás natural, sujeitas a diversas restrições e a incertezas técnicas e econômicas. Como não há como assegurar que os resultados dos projetos ocorram conforme o previsto, é possível que seu retorno seja inferior ao esperado, o que, dependendo da relevância, pode provocar um efeito adverso no resultado operacional e nas condições financeiras da companhia. Nesse mérito, a dissertação apresenta e aplica um modelo de programação estocástica linear inteira mista para seleção de portfólio de projetos que permita a maximização dos resultados, com restrição de risco. A aplicação considerou dados realistas do segmento de upstream de uma empresa do setor. Para representar os cenários econômicos, optou-se pela utilização da simulação de Monte Carlo do modelo Movimento Geométrico Browniano. Com o Valor Presente Líquido como retorno e Conditional Value-at-Risk representando a medida de risco, foi possível estabelecer a fronteira eficiente do risco-retorno, com a qual o decisor pode definir uma solução de portfólio, conforme sua aversão ao risco. / [en] In their multi-annual investment planning, oil and gas companies consider alternatives of production projects, subject to a variety of constraints, and technical and economic uncertainties. Considering that it is not possible to guarantee that these projects will perform as predicted, the return can be less than expected and can lead to a significant adverse effect to the operational results and to financial conditions of a given organization. Therefore, this dissertation proposes a mixed integer linear stochastic programming model for project portfolio selection that maximizes the return with risk constraint. The application considered realistic data from the upstream segment of an oil and gas company. Monte Carlo simulation of the Geometric Brownian Motion model was considered to represent the economic scenarios. Using the Net Present Value as the function and Conditional Value-at-Risk as a risk measure, it was possible to establish the efficient frontier of risk-return, which can assist the decision-maker to define the project portfolio according to their risk aversion.