Related papers: Optimal nonparametric estimation of the expected s…
We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As it is well known, one can map this problem into a linear programming setting. For some values of the external…
For nonparametric regression in the streaming setting, where data constantly flow in and require real-time analysis, a main challenge is that data are cleared from the computer system once processed due to limited computer memory and…
Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…
The problem of estimating the directed information rate between two discrete processes $\{X_n\}$ and $\{Y_n\}$ via the plug-in (or maximum-likelihood) estimator is considered. When the joint process $\{(X_n,Y_n)\}$ is a Markov chain of a…
We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed…
The best-known and most commonly used distribution-property estimation technique uses a plug-in estimator, with empirical frequency replacing the underlying distribution. We present novel linear-time-computable estimators that significantly…
Expected Shortfall (ES), also known as superquantile or Conditional Value-at-Risk, has been recognized as an important measure in risk analysis and stochastic optimization, and is also finding applications beyond these areas. In finance, it…
This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a…
We study the excess minimum risk in statistical inference, defined as the difference between the minimum expected loss in estimating a random variable from an observed feature vector and the minimum expected loss in estimating the same…
Expectile bears some interesting properties in comparison to the industry wide expected shortfall in terms of assessment of tail risk. We study the relationship between expectile and expected shortfall using duality results and the link to…
Expected Shortfall (ES), the average loss above a high quantile, is the current financial regulatory market risk measure. Its estimation and optimization are highly unstable against sample fluctuations and become impossible above a critical…
Utility-Based Shortfall Risk (UBSR) is a risk metric that is increasingly popular in financial applications, owing to certain desirable properties that it enjoys. We consider the problem of estimating UBSR in a recursive setting, where…
We study the problem of estimating a distribution over a finite alphabet from an i.i.d. sample, with accuracy measured in relative entropy (Kullback-Leibler divergence). While optimal bounds on the expected risk are known, high-probability…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
Given a dataset an outlier can be defined as an observation that it is unlikely to follow the statistical properties of the majority of the data. Computation of the location estimate of is fundamental in data analysis, and it is well known…
This paper attempts to provide a decision-theoretic foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. The main result is that the…
The issue of constructing a risk minimizing hedge under an additional almost-surely type constraint on the shortfall profile is examined. Several classical risk minimizing problems are adapted to the new setting and solved. In particular,…
Systemic risk measures have been shown to be predictive of financial crises and declines in real activity. Thus, forecasting them is of major importance in finance and economics. In this paper, we propose a new forecasting method for…
We consider removing lower order statistics from the classical Hill estimator in extreme value statistics, and compensating for it by rescaling the remaining terms. Trajectories of these trimmed statistics as a function of the extent of…
Forecast evaluations aim to choose an accurate forecast for making decisions by using loss functions. However, different loss functions often generate different ranking results for forecasts, which complicates the task of comparisons. In…