Multistage stochastic programming is an important tool in medium to long term planning where there are uncertainties in the data. In this thesis, we consider a special case of multistage stochastic programming in which each subprogram is a convex quadratic program. The results are also applicable if the quadratic objectives are replaced by convex piecewise quadratic functions. Convex piecewise quadratic functions have important application in financial planning problems as they can be used as very flexible risk measures. The stochastic programming problems can be used as multi-period portfolio planning problems tailored to the need of individual investors. Using techniques from convex analysis and sensitivity analysis, we show that each subproblem of a multistage quadratic stochastic program is a polyhedral piecewise quadratic program with convex Lipschitz objective. The objective of any subproblem is differentiable with Lipschitz gradient if all its descendent problems have unique dual variables, which can be guaranteed if the linear independence constraint qualification is satisfied. Expression for arbitrary elements of the subdifferential and generalized Hessian at a point can be calculated for quadratic pieces that are active at the point. Generalized Newton methods with linesearch are proposed for solving multistage quadratic stochastic programs. The algorithms converge globally. If the piecewise quadratic objective is differentiable and strictly convex at the solution, then convergence is also finite. A generalized Newton algorithm is implemented in Matlab. Numerical experiments have been carried out to demonstrate its effectiveness. The algorithm is tested on random data with 3, 4 and 5 stages with a maximum of 315 scenarios. The algorithm has also been successfully applied to two sets of test data from a capacity expansion problem and a portfolio management problem. Various strategies have been implemented to improve the efficiency of the proposed algorithm. We experimented with trust region methods with different parameters, using an advanced solution from a smaller version of the original problem and sorting the stochastic right hand sides to encourage faster convergence. The numerical results show that the proposed generalized Newton method is a highly accurate and effective method for multistage quadratic stochastic programs. For problems with the same number of stages, solution times increase linearly with the number of scenarios.

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Thesis (Ph.D. - Civil Engineering and Engineering Mechanics)--University of Arizona. / There are two pages numbered "70". Includes bibliographical references (leaves 184-188).

Thesis (Ph. D. in Operations Research)--Naval Postgraduate School, Sept. 2004. / Thesis Advisor(s): R. Kevin Wood. Includes bibliographical references (p. 71-80). Also available online.

Diss.: University of Duisburg-Essen, 2009. / Includes bibliographical references (p. [127]-134).

Thesis (Ph. D.)--Washington State University, August 2006. / Includes bibliographical references.

Wong Man Hong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 60-63). / Abstracts in English and Chinese. / Abstract --- p.i / Abstract in Chinese --- p.ii / Thesis Assessment Committee --- p.iii / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Our Work and Motivation --- p.1 / Chapter 1.2 --- Literature Review --- p.3 / Chapter 1.3 --- Thesis Structure --- p.5 / Chapter 2 --- Preliminary --- p.6 / Chapter 2.1 --- Calculus for Volume of Sphere --- p.6 / Chapter 2.2 --- Fractional Programming and Dinkelbach's Algorithm --- p.7 / Chapter 2.3 --- Nonlinear Programming and Interior Point Algorithm --- p.8 / Chapter 2.4 --- Second Order Cones and Conic Programming --- p.10 / Chapter 3 --- The Probability Model --- p.12 / Chapter 3.1 --- Derive the Chance Constraint --- p.12 / Chapter 3.2 --- Single Cluster Model --- p.18 / Chapter 3.3 --- Multi-clusters Model --- p.21 / Chapter 4 --- The Downside Risk Model --- p.24 / Chapter 4.1 --- Derive the Downside Risk Measure --- p.24 / Chapter 4.2 --- Calculate the First and Second Derivative of the Downside Risk --- p.27 / Chapter 4.3 --- Single Cluster Model and Numerical Algorithm --- p.29 / Chapter 4.4 --- Multi-clusters Model --- p.34 / Chapter 5 --- The Conditional Value-at-Risk Model --- p.37 / Chapter 5.1 --- Derive the Conditional Value at Risk --- p.37 / Chapter 5.2 --- Single Cluster Model and Numerical Algorithm --- p.41 / Chapter 5.3 --- Multi-clusters Model --- p.47 / Chapter 6 --- Numerical Results --- p.51 / Chapter 6.1 --- Data Set --- p.51 / Chapter 6.2 --- The Probability Model --- p.53 / Chapter 6.3 --- The Downside Risk Model --- p.53 / Chapter 6.4 --- The CVaR Model --- p.56 / Chapter 7 --- Conclusions --- p.58 / Bibliography --- p.60

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

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