相关论文: Risk Quantization by Magnitude and Propensity

If a given aggregate process $S$ is a compound mixed renewal process under a probability measure $P$, we provide a characterization of all probability measures $Q$ on the domain of $P$ such that $Q$ and $P$ are progressively equivalent and…

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…

This paper extends quantile factor analysis to a probabilistic variant that incorporates regularization and computationally efficient variational approximations. We establish through synthetic and real data experiments that the proposed…

Our investigation concerns the estimation of predictive densities and a study of efficiency as measured by the frequentist risk of such predictive densities with integrated $L_2$ and $L_1$ losses. Our findings relate to a $p-$variate…

We develop a novel stochastic valuation and premium calculation principle based on probability measure distortions that are induced by quantile processes in continuous time. Necessary and sufficient conditions are derived under which the…

The two statistical methods, namely the frequentist and the Bayesian methods, are both commonly used for probabilistic inference in many scientific situations. However, it is not straightforward to interpret the result of one approach in…

By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…

Procyclicality of historical risk measure estimation means that one tends to over-estimate future risk when present realized volatility is high and vice versa under-estimate future risk when the realized volatility is low. Out of it…

We consider the problem of determining an upper bound for the value of a spectral risk measure of a loss that is a general nonlinear function of two factors whose marginal distributions are known, but whose joint distribution is unknown.…

We address measurement error bias in propensity score (PS) analysis due to covariates that are latent variables. In the setting where latent covariate $X$ is measured via multiple error-prone items $\mathbf{W}$, PS analysis using several…

We study distributionally robust quantile regression using type-$p$ Wasserstein ambiguity sets. We derive a closed-form expression for the worst-case quantile regression loss under general $p$-Wasserstein uncertainty. We further give a…

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…

We establish conditions to characterize probability measures by their $L^{p}$-quantization error functions in both $\mathbb{R}^{d}$ and Hilbert settings. This characterization is two-fold: static (identity of two distributions) and dynamic…

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…

Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…

We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability measures hidden behind a given set of…

Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…

This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes…

Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of…

The paper has 2 main goals: 1. We propose a variant of the CAPM based on coherent risk. 2. In addition to the real-world measure and the risk-neutral measure, we propose the third one: the extreme measure. The introduction of this measure…