248 research outputs found
Output analysis for approximated stochastic programs
Because of incomplete information and also for the sake of numerical tractability one mostly solves an approximated stochastic program instead of the underlying ''true'' decision problem. However, without an additional analysis, the obtained output (the optimal value and optimal solutions of the approximated stochastic program) should not be used to replace the sought solution of the ''true'' problem. Methods of output analysis have to be tailored to the structure of the problem and they should also reflect the source, character and precision of the input data. The scope of various approaches based on results of asymptotic and robust statistics, of the moment problem and on general results of parametric programming will be discussed from the point of view of their applicability and possible extensions
On Stability of Multistage Stochastic Programs
We study quantitative stability of linear multistage stochastic programs underperturbations of the underlying stochastic processes. It is shown that the optimalvalues behave Lipschitz continuous with respect to an -distance. Therefore, wehave to make a crucial regularity assumption on the conditional distributions, thatallows to establish continuity of the recourse function with respect to the currentstate of the stochastic process. The main stability result holds for nonanticipativediscretizations of the underlying process and thus represents a rigorous justiïŹcationof established discretization techniques
Distribution Sensitivity Analysis for Stochastic Programs with Recourse
In this paper we study the stability of solutions to stochastic programming problems with recourse and show the Lipschitz continuity of optimal solutions as well as the associated Lagrange multipliers with respect to the distribution function
Incorporating statistical model error into the calculation of acceptability prices of contingent claims
The determination of acceptability prices of contingent claims requires the
choice of a stochastic model for the underlying asset price dynamics. Given
this model, optimal bid and ask prices can be found by stochastic optimization.
However, the model for the underlying asset price process is typically based on
data and found by a statistical estimation procedure. We define a confidence
set of possible estimated models by a nonparametric neighborhood of a baseline
model. This neighborhood serves as ambiguity set for a multi-stage stochastic
optimization problem under model uncertainty. We obtain distributionally robust
solutions of the acceptability pricing problem and derive the dual problem
formulation. Moreover, we prove a general large deviations result for the
nested distance, which allows to relate the bid and ask prices under model
ambiguity to the quality of the observed data.Comment: 27 pages, 2 figure
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