O processo de escolha de portfólios é um problema clássico da área financeira. Neste problema, o investidor busca aplicar seu dinheiro em um mercado de ações de forma a obter um bom compromisso entre o retorno esperado e o risco. Em geral, quanto maior o retorno esperado da carteira, maior o risco a ela associado. Neste trabalho foram estudadas modelagens para o problema de escolha de portfólio ótimo e suas aplicações ao mercado brasileiro. Do ponto de vista de modelagem foi proposta a inclusão do risco diversificável e não-diversificável ao modelo linear estudado. O risco diversificável foi incluído através de uma restrição que impõe um número mínimo de ativos na composição do portfólio ótimo, enquanto o risco não-diversificável foi adicionado considerando o beta da carteira. Do ponto de vista de aplicação, foi considerada a atribuição de valores de probabilidade para os retornos históricos dos ativos utilizados na análise do problema, visando incorporar informações do comportamento apresentado pelo mercado nos resultados. Na geração dos resultados, foram desenvolvidos em CPLEX um método ótimo de solução para o problema e um método para geração de uma curva de soluções Pareto ótimas / The process of selecting a portfolio is a classical problem in finance, where the investor intends to invest money in the stock market in such way that a reasonable trade-off between expected return and risk is obtained. In general, the higher the expected return of the portfolio is, the higher his risk will be. In this work the single period portfolio optimization problem is studied in terms of modeling and application for the Brazilian stock market. Referring to the model, changes are proposed to include the diversifiable and nondiversifiable risk. The diversifiable risk is included by imposing a minimum number of assets on the portfolio, while the nondiversifiable risk is controlled by restricting the portfolios beta. On the applications side, a method to estimate the probability of the assets historical returns is proposed, so more information about the market behavior is considered on the problem. The results were obtained by a optimal method to find the best solution and another one to generate the Pareto-optimal solutions, both developed using CPLEX

O processo de escolha de portfólios é um problema clássico da área financeira. Neste problema, o investidor busca aplicar seu dinheiro em um mercado de ações de forma a obter um bom compromisso entre o retorno esperado e o risco. Em geral, quanto maior o retorno esperado da carteira, maior o risco a ela associado. Neste trabalho foram estudadas modelagens para o problema de escolha de portfólio ótimo e suas aplicações ao mercado brasileiro. Do ponto de vista de modelagem foi proposta a inclusão do risco diversificável e não-diversificável ao modelo linear estudado. O risco diversificável foi incluído através de uma restrição que impõe um número mínimo de ativos na composição do portfólio ótimo, enquanto o risco não-diversificável foi adicionado considerando o beta da carteira. Do ponto de vista de aplicação, foi considerada a atribuição de valores de probabilidade para os retornos históricos dos ativos utilizados na análise do problema, visando incorporar informações do comportamento apresentado pelo mercado nos resultados. Na geração dos resultados, foram desenvolvidos em CPLEX um método ótimo de solução para o problema e um método para geração de uma curva de soluções Pareto ótimas / The process of selecting a portfolio is a classical problem in finance, where the investor intends to invest money in the stock market in such way that a reasonable trade-off between expected return and risk is obtained. In general, the higher the expected return of the portfolio is, the higher his risk will be. In this work the single period portfolio optimization problem is studied in terms of modeling and application for the Brazilian stock market. Referring to the model, changes are proposed to include the diversifiable and nondiversifiable risk. The diversifiable risk is included by imposing a minimum number of assets on the portfolio, while the nondiversifiable risk is controlled by restricting the portfolios beta. On the applications side, a method to estimate the probability of the assets historical returns is proposed, so more information about the market behavior is considered on the problem. The results were obtained by a optimal method to find the best solution and another one to generate the Pareto-optimal solutions, both developed using CPLEX

Limited freshwater supply is the most important challenge in water resources management, particularly in arid and semi-arid basins. However, other variations in a basin, including climate change, population growth, and economic development intensify this threat to water security. The Oldman River Basin (OMRB), located in southern Alberta, Canada, is a semi-arid basin and encompasses several water challenges, including uncertain water supply as well as increasing, uncertain water demands (consumptive irrigation, municipal, and industrial demands, and non-consumptive hydropower generation, and environmental demands). Reservoirs, of which the Oldman River Reservoir is the largest in the basin, are responsible for meeting most of demands, and, protecting the basin’s economy. The OMRB has also faced extreme natural events, floods and droughts, in the past, which reservoir management plays a critical role to adapt to. The complexity of the climate, hydrology, and water resource system and water governance escalates the challenges in the basin. These factors are highly interconnected and establish dynamic, non-linear behavior, which requires an integrated, feedback-based tool to investigate. Integrated water resources (IWRM) modelling using system dynamics (SD) is such an approach to tackle the different water challenges and understand their non-linear, dynamic pattern. In this research study the Sustainability-oriented Water Allocation, Management, and Planning (SWAMPOM) model for the Oldman River Basin is developed. SWAMPOM comprises a water allocation model, dynamic irrigation demand, instream flow needs (IFN), and economic evaluation sub-models. The water allocation model allocates water to all the above-mentioned demands at a weekly time step from 1928 to 2001, and under different water availability scenarios. Meeting irrigation demands relies on the crop water requirement (CWR), which is calculated under different climatic conditions by the dynamic irrigation demand sub-model. This sub-model estimates the weekly irrigation demand for main crops planted in the basin. SWAMPOM also computes environmental demands or instream flow need (IFN) for the Oldman River, and allocates water to rivers to meet IFN under different policy scenarios and uncertain water supply. Finally, the major water-related economic benefit in the basin, earned by agriculture and hydropower generation, is computed by the economic evaluation sub-model. The results show that SWAMPOM could reasonably satisfy the demands at a weekly time step and provide an adequate estimation of the crop water requirement under different hydrometeorological conditions. Based on the SWAMPOM’s results, the average annual irrigation demand is 306 mm over the historical time period from 1928 to 2001 in the main irrigation districts. The average weekly instream flow need of the Oldman River is calculated to be approximately 20.5 m3/s, which can be met in more than 97% of weeks in the historical time period. Average annual water-related economic benefit was computed to be 192.5 M$ in the OMRB. It decreased to 82.8 M$ in very dry years, and increased up to 328.6 M$ in very wet years. This research also developed different sets of Oldman Reservoir’s operation zones, resulting in trade-offs between the optimal economic benefit, water allocated to the ecosystem, minimum floodwater and minimum flood frequency. This helps decision makers to decide how much water should be stored in the reservoir to meet a specific objective while not sacrificing others. A multi-objective performance assessment, Pareto curve approach, is applied to identify the optimal trade-offs between the four objective functions (OFs), and 18 different optimal, or close to optimal sets of operating zones are provided. The decision regarding the operating zones depends on decision makers’ preference for higher economic benefit, water allocated to IFN, or flood security. However, the set of operating zones with minimum floodwater causes 11 less flood events; the operating zones with maximum economic benefits result in 4.1% more financial gain; and the zones with maximum water allocated to IFN lead to 10.1% more ecosystem protection in the whole 74 years, compared to current zones.