In this thesis, we consider a sampling design problem for a distributed parameter estimation system. The system contains a number of remotely located local sensors that can preprocess the observed signal and convey the processed data to a data fusion center to make the final estimate. Two issues are considered for this system. One is a sampling scheme design for a parameter estimation problem in a single context. The other is how to assign the appropriate number of sampling points to each of the sensors when a constraint on the total sample size is assumed. Here we propose to design this two issues by maximizing the criterion of Fisher's information or minimizing the Fisher's information loss . A sampling design procedure will be established and some numerical simulations will be also carried out for illustration purpose.

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The distribution system which forms the final connection between customers and power source plays a vital role in an electrical network. Different studies show that substantial proportion of the customer interruptions occurs due to the failures on distribution network. The ongoing privatization process of the electrical distribution services in Turkey raises the importance of reliable and continuous electricity supply significantly. The new regulations come up with this privatization process and the electrical distribution companies are strictly required to comply with these regulations to ensure the reliability of the distribution network. The legal framework and severe punishments applied to the electrical distribution companies exceeding the continuity of supply indices force them to invest on their network in order to increase the reliability of their system. As the reliability of electricity supplied increases, investment cost also increases. However, low system reliability causes higher outage frequency and duration which will increase the damage of these outages to customers and also increases the cost of the distribution company as a result of the penalty payments. This tradeoff between Outage Cost and Utility Cost requires consideration of an optimization when determining the optimal reliability level. In rural areas where electrical distribution network consists of long radial overhead lines in arborescent structure, continuity of supply is a major problem due to the high failure rates. The implementation of protection devices having reclosing capability and automated sectionalizing switches enhances the continuity of supply on rural networks substantially. The balance between the cost associated with installation of switches and the reduction on Outage Cost is an important optimization issue for distribution network operators. In this thesis study an algorithm is developed in order to determine the optimum number and locations of the sectionalizing switches on a rural electrical distribution network in Turkey which gives an optimum investment level with an optimum Outage Cost.

Este trabalho apresenta a aplicação de uma abordagem via programação estocástica linear para definição da alocação de ativos ótima em um fundo de investimento estruturado. A carteira adotada é formada por caixa, futuro de Ibovespa e call de Ibovespa. A partir da definição da alocação ótima é feita uma análise do sucesso dessa carteira em superar a performance do índice Bovespa. Além disso, é feita uma análise comparativa contra uma carteira formada apenas por caixa e um ativo com retorno igual ao do índice Bovespa à vista. Tal comparação analisa a diferença de performance e também a diferença de risco medido pelo VaR (value at risk) versus retorno. A metodologia adotada para obtenção da alocação ótima é baseada na geração de uma árvore de cenários de parâmetros de mercado sobre a qual os ativos que formam a carteira são revalorizados de tal modo que o lucro acumulado ao fim do prazo de vida do fundo seja maximizado. Os resultados obtidos mostram que a performance da carteira formada por caixa, futuros e calls supera a performance da carteira formada por caixa e índice Bovespa à vista mesmo quando sujeito a um mesmo nível de risco. Além disso, a metodologia de comparação proposta neste trabalho também se mostrou bastante útil na prática de tomada de decisões de investimento por permitir comparar a performance de estratégias de investimentos dinâmicas. / This paper presents an application that uses linear stochastic programming to define the optimal asset allocation of an structured investment fund. The portfolio adopted is comprised of cash, Ibovespa futures and calls of Ibovespa. The performance of the portfolio with optimal allocation is compared to the performance of Bovespa index. Moreover, the performance of the portfolio with optimal allocation is also compared with that of a portfolio comprised of cash and a risky asset with return equal to the Bovespa index return. Such analysis highlights not only the differences of performance but also the differences of the associated risk level measured by the VaR (Value at Risk) versus return. The methodology used for obtaining the optimal allocation is based on an event tree of market parameters, which is used to reprice the assets comprising the portfolio so that the total profit at the end of the funds life is maximized. The results show that the portfolio comprised of cash, Ibovespa futures and calls of Ibovespa outperforms the Bovespa index and also the portfolio comprised of cash and Bovespa index even when subject to the same level of risk. The analysis developed in this paper allows the comparison between dynamic investment strategies, which can be very useful on practical decision making process of asset and liability management.

Este trabalho apresenta a aplicação de uma abordagem via programação estocástica linear para definição da alocação de ativos ótima em um fundo de investimento estruturado. A carteira adotada é formada por caixa, futuro de Ibovespa e call de Ibovespa. A partir da definição da alocação ótima é feita uma análise do sucesso dessa carteira em superar a performance do índice Bovespa. Além disso, é feita uma análise comparativa contra uma carteira formada apenas por caixa e um ativo com retorno igual ao do índice Bovespa à vista. Tal comparação analisa a diferença de performance e também a diferença de risco medido pelo VaR (value at risk) versus retorno. A metodologia adotada para obtenção da alocação ótima é baseada na geração de uma árvore de cenários de parâmetros de mercado sobre a qual os ativos que formam a carteira são revalorizados de tal modo que o lucro acumulado ao fim do prazo de vida do fundo seja maximizado. Os resultados obtidos mostram que a performance da carteira formada por caixa, futuros e calls supera a performance da carteira formada por caixa e índice Bovespa à vista mesmo quando sujeito a um mesmo nível de risco. Além disso, a metodologia de comparação proposta neste trabalho também se mostrou bastante útil na prática de tomada de decisões de investimento por permitir comparar a performance de estratégias de investimentos dinâmicas. / This paper presents an application that uses linear stochastic programming to define the optimal asset allocation of an structured investment fund. The portfolio adopted is comprised of cash, Ibovespa futures and calls of Ibovespa. The performance of the portfolio with optimal allocation is compared to the performance of Bovespa index. Moreover, the performance of the portfolio with optimal allocation is also compared with that of a portfolio comprised of cash and a risky asset with return equal to the Bovespa index return. Such analysis highlights not only the differences of performance but also the differences of the associated risk level measured by the VaR (Value at Risk) versus return. The methodology used for obtaining the optimal allocation is based on an event tree of market parameters, which is used to reprice the assets comprising the portfolio so that the total profit at the end of the funds life is maximized. The results show that the portfolio comprised of cash, Ibovespa futures and calls of Ibovespa outperforms the Bovespa index and also the portfolio comprised of cash and Bovespa index even when subject to the same level of risk. The analysis developed in this paper allows the comparison between dynamic investment strategies, which can be very useful on practical decision making process of asset and liability management.

Many insurance and finance activities involve multiple risks. Dependence structures between different risks play an important role in both theoretical models and practical applications. However, stochastic and actuarial models with dependence are very challenging research topics. In most literature, only special dependence structures have been considered. However, most existing special dependence structures can be integrated into more-general contexts. This thesis is motivated by the desire to develop more-general dependence structures and to consider their applications. This thesis systematically studies different dependence notions and explores their applications in the fields of insurance and finance. It contributes to the current literature in the following three main respects. First, it introduces some dependence notions to actuarial science and initiates a new approach to studying optimal reinsurance problems. Second, it proposes new notions of dependence and provides a general context for the studies of optimal allocation problems in insurance and finance. Third, it builds the connections between copulas and the proposed dependence notions, thus enabling the constructions of the proposed dependence structures and enhancing their applicability in practice. The results derived in the thesis not only unify and generalize the existing studies of optimization problems in insurance and finance, but also admit promising applications in other fields, such as operations research and risk management.

Many insurance and finance activities involve multiple risks. Dependence structures between different risks play an important role in both theoretical models and practical applications. However, stochastic and actuarial models with dependence are very challenging research topics. In most literature, only special dependence structures have been considered. However, most existing special dependence structures can be integrated into more-general contexts. This thesis is motivated by the desire to develop more-general dependence structures and to consider their applications. This thesis systematically studies different dependence notions and explores their applications in the fields of insurance and finance. It contributes to the current literature in the following three main respects. First, it introduces some dependence notions to actuarial science and initiates a new approach to studying optimal reinsurance problems. Second, it proposes new notions of dependence and provides a general context for the studies of optimal allocation problems in insurance and finance. Third, it builds the connections between copulas and the proposed dependence notions, thus enabling the constructions of the proposed dependence structures and enhancing their applicability in practice. The results derived in the thesis not only unify and generalize the existing studies of optimization problems in insurance and finance, but also admit promising applications in other fields, such as operations research and risk management.

Response adaptive randomization represents a major advance in clinical trial methodology that helps balance the benefits of the collective and the benefits of the individual and improves efficiency without undermining the validity and integrity of the clinical research. Response adaptive designs use information so far accumulated from the trial to modify the randomization procedure and deliberately bias treatment allocation in order to assign more patients to the potentially better treatment. No attention has been paid to incorporating the problem of errors-in-variables in adaptive clinical trials. In this work, some important issues and methods of response adaptive design of clinical trials in the presence of mismeasurement are examined. We formulate response adaptive designs when the dichotomous response may be misclassified. We consider the optimal allocations under various objectives, investigate the asymptotically best response adaptive randomization procedure, and discuss effects of misclassification on the optimal allocation. We derive explicit expressions for the variance-penalized criterion with misclassified binary responses and propose a new target proportion of treatment allocation under the criterion. A real-life clinical trial and some related simulation results are also presented.

Response adaptive randomization represents a major advance in clinical trial methodology that helps balance the benefits of the collective and the benefits of the individual and improves efficiency without undermining the validity and integrity of the clinical research. Response adaptive designs use information so far accumulated from the trial to modify the randomization procedure and deliberately bias treatment allocation in order to assign more patients to the potentially better treatment. No attention has been paid to incorporating the problem of errors-in-variables in adaptive clinical trials. In this work, some important issues and methods of response adaptive design of clinical trials in the presence of mismeasurement are examined. We formulate response adaptive designs when the dichotomous response may be misclassified. We consider the optimal allocations under various objectives, investigate the asymptotically best response adaptive randomization procedure, and discuss effects of misclassification on the optimal allocation. We derive explicit expressions for the variance-penalized criterion with misclassified binary responses and propose a new target proportion of treatment allocation under the criterion. A real-life clinical trial and some related simulation results are also presented.

Monitoring population trend and estimating vital demographic parameters are essential for effective management of a mule deer (Odocoileus hemionus) population. Because of financial constraints, many wildlife agencies use computer models to obtain indirect indices of population size and trend as an alternative to annual field-based estimates of population size. These models are based primarily on herd composition counts and harvest rates from hunter-harvest surveys, and are rarely field validated. I developed an alternative method for monitoring population dynamics of wintering populations of mule deer. I designed a hybrid monitoring program that combined annual vital rate monitoring to track changes in population growth rate with a field-based approach for estimating population abundance. The program allocated resources optimally towards the most critical components of mule deer population dynamics, and consisted of 4 field surveys: annual monitoring of age ratios, overwinter fawn survival, and annual doe survival, with field-based estimates of population size only once every 4 years. Surveys were conducted from 2006 to 2008 in Wildlife Management Unit (WMU) 2, Utah, and cost $29,298 per year, prorated over 4 years. Unfortunately, financial constraints prohibit the implementation of this monitoring program in every WMU in Utah. Instead, the program can be implemented in select WMUs throughout the state, with survival data collected in these core units, providing estimates for nearby satellite units. To establish core-satellite unit pairs, I developed a proxy method for determining correlation in survival rates between core and satellite units using model-simulated estimates. I demonstrated this core-satellite method using WMU 2 as a core and WMU 3, an adjacent unit, as a satellite. Finally, I compared a multiple data sources (MDS) model with a herd composition-based population model, POP-II. The MDS model better approximated observed data, and provided statistical rigor. Overall, the hybrid program was less costly and provided more precise estimates of population trend than could be achieved with a monitoring program focused on abundance alone, and was more defensible than herd composition monitoring. After establishing correlations in doe and fawn survival between core and satellite units, data collected in core units via the hybrid program could then be used to model the mule deer population dynamics of other units using MDS modeling procedures. This combined approach could be an effective statewide program for monitoring mule deer populations.