Abstract
In this chapter we consider again the basic multistage decision problem
or in extensive form
where Q is the cost function, \(\mathbb{X}\) is the feasible set of decision functions, \(\mathcal{R}_{\mathbb{P}}\) is a risk functional, and \(\mathbb{P}\) is the probability model (a nested distribution).
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Notes
- 1.
- 2.
The notation refers to the finite case, where P is a row vector and the transportation kernel K is a Markovian transition matrix but may of course be extended to the general case.
- 3.
See also the paper [4] forthcoming in Computational Management Science 2014.
- 4.
More precisely: the saddle point set contains a \(\mathbb{P}^{{\ast}}\) , which is in \(\mathcal{P}_{\epsilon }\).
- 5.
The numerical example is taken from AIMMS optimization modeling [12, Chapter 17]. However, all computational procedures, solution algorithms, and resulting analysis are implemented in MATLAB R2012a. The implementations are due to Bita Analui.
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Pflug, G.C., Pichler, A. (2014). The Problem of Ambiguity in Stochastic Optimization. In: Multistage Stochastic Optimization. Springer Series in Operations Research and Financial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-08843-3_7
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