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pro vyhledávání: '"Kraetschmer, Volker"'
Autor:
Krätschmer, Volker
We study statistical properties of the optimal value of the Sample Average Approximation. The focus is on the tail function of the absolute error induced by the Sample Average Approximation, deriving upper estimates of its outcomes dependent on the s
Externí odkaz:
http://arxiv.org/abs/2301.05539
Autor:
Krätschmer, Volker
We investigate statistical properties of the optimal value of the Sample Average Approximation of stochastic programs, continuing the study in Kr\"atschmer (2023). Central Limit Theorem type results are derived for the optimal value. As a crucial poi
Externí odkaz:
http://arxiv.org/abs/2107.13863
Autor:
Belomestny, Denis, Kraetschmer, Volker
In this paper we give sufficient conditions guaranteeing the validity of the well-known minimax theorem for the lower Snell envelope with respect to a family of absolutely continuous probability measures. Such minimax results play an important role i
Externí odkaz:
http://arxiv.org/abs/1708.08904
Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of risk. From t
Externí odkaz:
http://arxiv.org/abs/1611.08434
We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions when the sto
Externí odkaz:
http://arxiv.org/abs/1603.07384
Autor:
Krätschmer, Volker, Zähle, Henryk
Expectiles were introduced by Newey and Powell (1987) in the context of linear regression models. Recently, Bellini et al. (2014) revealed that expectiles can also be seen as reasonable law-invariant risk measures. In this article, we show that the c
Externí odkaz:
http://arxiv.org/abs/1601.05261
Many standard estimators such as several maximum likelihood estimators or the empirical estimator for any law-invariant convex risk measure are not (qualitatively) robust in the classical sense. However, these estimators may nevertheless satisfy a we
Externí odkaz:
http://arxiv.org/abs/1511.08677
Autor:
Belomestny, Denis, Kraetschmer, Volker
In this paper we study optimal stopping problems with respect to distorted expectations of the form \begin{eqnarray*} \mathcal{E}(X)=\int_{-\infty}^{\infty} x\,dG(F_X(x)), \end{eqnarray*} where $F_X$ is the distribution function of $X$ and $G$ is a c
Externí odkaz:
http://arxiv.org/abs/1506.04439
Autor:
Belomestny, Denis, Kraetschmer, Volker
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel representatio
Externí odkaz:
http://arxiv.org/abs/1405.2240
We apply a suitable modification of the functional delta method to statistical functionals that arise from law-invariant coherent risk measures. To this end we establish differentiability of the statistical functional in a relaxed Hadamard sense, nam
Externí odkaz:
http://arxiv.org/abs/1401.3167