5,094 research outputs found
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 justiďŹcationof established discretization techniques
Evolutionary multi-stage financial scenario tree generation
Multi-stage financial decision optimization under uncertainty depends on a
careful numerical approximation of the underlying stochastic process, which
describes the future returns of the selected assets or asset categories.
Various approaches towards an optimal generation of discrete-time,
discrete-state approximations (represented as scenario trees) have been
suggested in the literature. In this paper, a new evolutionary algorithm to
create scenario trees for multi-stage financial optimization models will be
presented. Numerical results and implementation details conclude the paper
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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