Related papers: A new characterization of second-order stochastic …
We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…
The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…
This paper develops an axiomatic framework for ranking metrics, a general class of functionals for evaluating and ordering financial or insurance positions. Unlike traditional risk-adjusted performance measures-such as the Sharpe ratio,…
Stochastic ordering of distributions of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings, by iteratively reassigning tail-weights. The actual…
Stochastic dominance is a preference relation of uncertain prospect defined over a class of utility functions. While this utility class represents basic properties of risk aversion, it includes some extreme utility functions rarely…
We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…
In this paper, we establish some second order necessary/sufficient optimality conditions for optimal control problems of stochastic evolution equations in infinite dimensions. The control acts on both the drift and diffusion terms and the…
This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…
Our work is part of the close link between continuous-time dissipative dynamical systems and optimization algorithms, and more precisely here, in the stochastic setting. We aim to study stochastic convex minimization problems through the…
Model selection aims to identify a sufficiently well performing model that is possibly simpler than the most complex model among a pool of candidates. However, the decision-making process itself can inadvertently introduce non-negligible…
Risk measures connect probability theory or statistics to optimization, particularly to convex optimization. They are nowadays standard in applications of finance and in insurance involving risk aversion. This paper investigates a wide…
A classical result in risk measure theory states that every coherent risk measure has a dual representation as the supremum of certain expected value over a risk envelope. We study this topic in more detail. The related issues include: 1.…
The expectile can be considered as a generalization of quantile. While expected shortfall is a quantile based risk measure, we study its counterpart -- the expectile based expected shortfall -- where expectile takes the place of quantile.…
In this paper we apply second-order stochastic dominance (SSD) to the problem of enhanced indexation with asset subset (sector) constraints. The problem we consider is how to construct a portfolio that is designed to outperform a given…
The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn…
This paper aims to study a new stochastic order based upon discrete Laplace transforms. By this order, in a setup where the sample size is random, having discrete delta and nabla distributions, we obtain some ordering results involving…
Acquisition of data is a difficult task in many applications of machine learning, and it is only natural that one hopes and expects the population risk to decrease (better performance) monotonically with increasing data points. It turns…
Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that is generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first…
Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the…
Many results on the convex order in the literature were stated for random variables with finite mean. For instance, a fundamental result in dependence modeling is that the sum of a pair of random random variables is upper bounded in convex…