Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 89-95).

Zugl.: Duisburg, Essen, Univ., Diss., 2008

Thesis (Ph.D)--Architecture, Georgia Institute of Technology, 2010. / Committee Chair: Godfried Augenbroe; Committee Member: Ellis Johnson; Committee Member: Pieter De Wilde; Committee Member: Ruchi Choudhary; Committee Member: Russell Gentry. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Title: Nonconvex stochastic programming problems - formulations, sample approximations and stability Author: RNDr. Martin Branda Author's e-mail address: branda@karlin.mff.cuni.cz Supervisor: Doc. RNDr. Petr Lachout, CSc. Supervisor's e-mail address: lachout@karlin.mff.cuni.cz Abstract: We deal with problems where integer variables may appear, hence no assumptions on convexity are made throughout this thesis. The goal of Chapter 2 is to introduce stochastic programming problems and to outline the most important tasks connected with solving the problems. In Chapter 3, we compare basic formulations of static stochastic programming problems with chance constraints, with integrated chance constraints and with penalties in the objective function. We show that the problems are asymptotically equivalent under mild conditions. We discuss solving the problems using sample approximation techniques and extend some results on rates of convergence. All the formulations and corresponding sample approximations are compared on an investment problem with real features with Value at Risk constraint, integer allocations and transaction costs. Then, stability of financial decision models where two-stage mixed-integer value function appears as a loss variable is studied. In Chapter 4, we study qualitative properties of the...

Este trabalho trata de uma aplicação de programação estocástica para administração de passivos e ativos. Inicialmente, um modelo de administração de ativos e passivos utilizando valores de retorno de ativos determinísticos é formalizado, constatando-se as suas limitações, justificando-se a necessidade de abranger formalmente a incerteza inerente aos mercados financeiros. Para isso, um modelo para administração de ativos e passivos que utiliza otimização e programação estocástica baseado em uma árvore de cenários multiestágio balanceada é apresentado, descrito, e implementado. Os seus resultados determinam uma política de investimento de ativos para o instante inicial do período considerado, definindo-se também uma regra que possibilita, a partir do equilíbrio entre o patrimônio inicial e total de passivo a ser pago ao final do período considerado, estimar a probabilidade de insolvência do fundo de pensão. Além disso, realiza-se o estudo do impacto da redução de uma proxy da taxa de juros básico na composição do portfólio administrado por essas empresas. / This work discusses an application of stochastic programming for asset-liability management. Initially, a deterministic asset-liability model is formalized. Its limitations become clear which justify the need to include uncertainty in the model. Then, a stochastic programming model based on a balanced multistage scenario tree is presented, described and implemented for an asset-liability environment. The main results are: (i) an investment policy for the fund, and, (ii) the pension’s fund insolvency probability considering an initial relation between the current assets and the present value of the future liabilities. The impact of a possible reduction in interested rate on the pension’s fund optimal portfolio is also presented.

Este trabalho trata de uma aplicação de programação estocástica para administração de passivos e ativos. Inicialmente, um modelo de administração de ativos e passivos utilizando valores de retorno de ativos determinísticos é formalizado, constatando-se as suas limitações, justificando-se a necessidade de abranger formalmente a incerteza inerente aos mercados financeiros. Para isso, um modelo para administração de ativos e passivos que utiliza otimização e programação estocástica baseado em uma árvore de cenários multiestágio balanceada é apresentado, descrito, e implementado. Os seus resultados determinam uma política de investimento de ativos para o instante inicial do período considerado, definindo-se também uma regra que possibilita, a partir do equilíbrio entre o patrimônio inicial e total de passivo a ser pago ao final do período considerado, estimar a probabilidade de insolvência do fundo de pensão. Além disso, realiza-se o estudo do impacto da redução de uma proxy da taxa de juros básico na composição do portfólio administrado por essas empresas. / This work discusses an application of stochastic programming for asset-liability management. Initially, a deterministic asset-liability model is formalized. Its limitations become clear which justify the need to include uncertainty in the model. Then, a stochastic programming model based on a balanced multistage scenario tree is presented, described and implemented for an asset-liability environment. The main results are: (i) an investment policy for the fund, and, (ii) the pension’s fund insolvency probability considering an initial relation between the current assets and the present value of the future liabilities. The impact of a possible reduction in interested rate on the pension’s fund optimal portfolio is also presented.

Este trabalho trata de uma aplicação de programação estocástica para administração de passivos e ativos. Inicialmente, um modelo de administração de ativos e passivos utilizando valores de retorno de ativos determinísticos é formalizado, constatando-se as suas limitações, justificando-se a necessidade de abranger formalmente a incerteza inerente aos mercados financeiros. Para isso, um modelo para administração de ativos e passivos que utiliza otimização e programação estocástica baseado em uma árvore de cenários multiestágio balanceada é apresentado, descrito, e implementado. Os seus resultados determinam uma política de investimento de ativos para o instante inicial do período considerado, definindo-se também uma regra que possibilita, a partir do equilíbrio entre o patrimônio inicial e total de passivo a ser pago ao final do período considerado, estimar a probabilidade de insolvência do fundo de pensão. Além disso, realiza-se o estudo do impacto da redução de uma proxy da taxa de juros básico na composição do portfólio administrado por essas empresas. / This work discusses an application of stochastic programming for asset-liability management. Initially, a deterministic asset-liability model is formalized. Its limitations become clear which justify the need to include uncertainty in the model. Then, a stochastic programming model based on a balanced multistage scenario tree is presented, described and implemented for an asset-liability environment. The main results are: (i) an investment policy for the fund, and, (ii) the pension’s fund insolvency probability considering an initial relation between the current assets and the present value of the future liabilities. The impact of a possible reduction in interested rate on the pension’s fund optimal portfolio is also presented.

This dissertation presents various aspects of the solution of the linear multi-period stochastic programming problem. Under relatively mild assumptions on the structure of the random variables present in the problem, the value function at every time stage is shown to be jointly convex in the history of the process, namely the random variables observed so far as well as the decisions taken up to that point. Convexity enables the construction of both upper and lower bounds on the value of the entire problem by suitable discretization of the random variables. These bounds are developed in Chapter 2, where it is also demonstrated how the bounds can be made arbitrarily sharp if the discretizations are chosen sufficiently fine. The chapter emphasizes computability of the bounds, but does not concern itself with finding the discretizations themselves. The practise commonly followed to obtain a discretization of a random variable is to partition its support, usually into rectangular subsets. In order to apply the bounds of Chapter 2, one needs to determine the probability mass and weighted centroid for each element of the partition. This is a hard problem in itself, since in the continuous case it amounts to a multi-dimensional integration. Chapter 3 describes some Monte-Carlo techniques which can be used for normal distributions. These methods require random sampling, and the two main issues addressed are efficiency and accuracy. It turns out that the optimal method to use depends somewhat on the probability mass of the set in question. Having obtained a suitable discretization, one can then solve the resulting large scale linear program which approximates the original problem. Its constraint matrix is highly structured, and Chapter 4 describes one algorithm which attempts to utilize this structure. The algorithm uses the Dantzig-Wolfe decomposition principle, nesting decomposition levels one inside the other. Many of the subproblems generated in the course of this decomposition share the same constraint matrices and can thus be solved simultaneously. Numerical results show that the algorithm may out-perform a linear programming package on some simple problems. Chapter 5, finally, combines all these ideas and applies them to a problem in forest management. Here it is required to find logging levels in each of several time periods to maximize the expected revenue, computed as the volume cut times an appropriate discount factor. Uncertainty enters into the model in the form of the risk of forest fires and other environmental hazards, which may destroy a fraction of the existing forest. Several discretizations are used to formulate both upper and lower bound approximations to the original problem. / Business, Sauder School of / Graduate

No description available.