Related papers: Representation Results for Law Invariant Recursive…
This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time…
Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of…
In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…
Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional…
We consider a distributionally robust stochastic optimization problem and formulate it as a stochastic two-level composition optimization problem with the use of the mean--semideviation risk measure. In this setting, we consider a single…
We propose a risk measurement approach for a risk-averse stochastic problem. We provide results that guarantee that our problem has a solution. We characterize and explore the properties of the argmin as a risk measure and the minimum as a…
Generalized variational inference (GVI) provides an optimization-theoretic framework for statistical estimation that encapsulates many traditional estimation procedures. The typical GVI problem is to compute a distribution of parameters…
We continue the study of random continued fraction expansions, generated by random application of the Gauss and the R\'enyi backward continued fraction maps. We show that this random dynamical system admits a unique absolutely continuous…
We design a recursive measure of voting power based on partial as well as full voting efficacy. Classical measures, by contrast, incorporate solely full efficacy. We motivate our design by representing voting games using a division lattice…
Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed…
In this paper we propose the notion of continuous-time dynamic spectral risk-measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk-measures in terms of certain backward stochastic…
We address the problem of sharing risk among agents with preferences modelled by a general class of comonotonic additive and law-based functionals that need not be either monotone or convex. Such functionals are called distortion…
We introduce a distributional method for learning the optimal policy in risk averse Markov decision process with finite state action spaces, latent costs, and stationary dynamics. We assume sequential observations of states, actions, and…
The aim of this note is to prove the inversion formula, which can be used to compute the Levi measure of an infinitely divisible distribution from its characteristic function. Obtained formula is similar to the well-known inversion formula…
Invariant Causal Prediction (Peters et al., 2016) is a technique for out-of-distribution generalization which assumes that some aspects of the data distribution vary across the training set but that the underlying causal mechanisms remain…
Domain generalization (DG) aims to learn predictive models that can generalize to unseen domains. Most existing DG approaches focus on learning domain-invariant representations under the assumption of conditional distribution shift (i.e.,…
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
In this paper, a new decay estimate for a class of stochastic evolution equations with weakly dissipative drifts is established, which directly implies the uniqueness of invariant measures for the corresponding transition semigroups.…