arXiv subjects

Linxiao Wei

Publications and source records attributed to Linxiao Wei.

4 recordsLinked to original sources

arXiv2025

On data-driven robust distortion risk measures for non-negative risks with partial information

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 characterized solely by a ball determined by general Wasserstein distance centered at certain empirical distribution function, and then further consider additional constraints of known first moment and any other higher moment of the underlying loss distribution function. Under the assumption that the distortion function is strictly concave and twice differentiable, and that the underlying loss random variable is non-negative and bounded, we derive closed-form expressions for the distribution functions which maximize a given distortion risk measure over the distributional uncertainty sets respectively. Moreover, we continue to study the general case of a concave distortion function and unbounded loss random variables. Comparisons with existing studies are also made. Finally, we provide a numerical study to illustrate the proposed models and results. Our work provides a novel generalization of several known achievements in the literature.

q-fin.RM↗

arXiv2024

Elicitability and identifiability of tail risk measures

Tail risk measures are fully determined by the distribution of the underlying loss beyond its quantile at a certain level, with Value-at-Risk, Expected Shortfall and Range Value-at-Risk being prime examples. They are induced by law-based risk measures, called their generators, evaluated on the tail distribution. This paper establishes joint identifiability and elicitability results of tail risk measures together with the corresponding quantile, provided that their generators are identifiable and elicitable, respectively. As an example, we establish the joint identifiability and elicitability of the tail expectile together with the quantile. The corresponding consistent scores constitute a novel class of weighted scores, nesting the known class of scores of Fissler and Ziegel for the Expected Shortfall together with the quantile. For statistical purposes, our results pave the way to easier model fitting for tail risk measures via regression and the generalized method of moments, but also model comparison and model validation in terms of established backtesting procedures.

q-fin.ST↗

arXiv2022

On evaluation of joint risk for non-negative multivariate risks under dependence uncertainty

In this paper, we propose a novel axiomatic approach to evaluating the joint risk of multiple insurance risks under dependence uncertainty. Motivated by both the theory of expected utility and the Cobb-Dauglas utility function, we establish a joint risk measure for non-negative multivariate risks, which we refer to as a scalar distortion joint risk measure. After having studied its fundamental properties, we provide an axiomatic characterization of it by proposing a set of new axioms. The most novel axiom is the component-wise positive homogeneity. Then, based on the resulting distortion joint risk measures, we also propose a new class of vector-valued distortion joint risk measures for non-negative multivariate risks. Finally, we make comparisons with some vector-valued multivariate risk measures known in the literature, such as multivariate lower-orthant value at risk, multivariate upper-orthant conditional-tail-expectation, multivariate tail conditional expectation and multivariate tail distortion risk measures. It turns out that those vector-valued multivariate risk measures have forms of vector-valued distortion joint risk measures, respectively. This paper mainly gives some theoretical results about the evaluation of joint risk under dependence uncertainty, and it is expected to be helpful for measuring joint risk.

q-fin.RM↗

arXiv2022

On conditional distortion risk measures under uncertainty

Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the model uncertainty, and thus propose a new class of risk measures under model uncertainty. More precisely, we use an auxiliary random variable to describe the model uncertainty. We first establish a conditional distortion risk measure under an auxiliary random variable. Then we axiomatically characterize it by proposing a set of new axioms. Moreover, its coherence and dual representation are investigated. Finally, we make comparisons with some known risk measures such as weighted value at risk (WVaR), range value at risk (RVaR) and $\sQ-$ mixture of ES. One advantage of our modeling is in its flexibility, as the auxiliary random variable can describe various contexts including model uncertainty. To illustrate the proposed framework, we also deduce new risk measures in the presence of background risk.This paper provides some theoretical results about risk measures under model uncertainty, being expected to make meaningful complement to the study of risk measures under model uncertainty.

econ.TH↗