Related papers: Asymptotic Analysis for Spectral Risk Measures Par…
The aggregation of individual risks in large credit and insurance portfolios is guided by diversification and the law of large numbers, which formalizes the convergence of sample averages to their means. At the same time, regulatory capital…
Risk assessment under different possible scenarios is a source of uncertainty that may lead to concerning financial losses. We address this issue, first, by adapting a robust framework to the class of spectral risk measures. Second, we…
Basel II and Solvency 2 both use the Value-at-Risk (VaR) as the risk measure to compute the Capital Requirements. In practice, to calibrate the VaR, a normal approximation is often chosen for the unknown distribution of the yearly log…
Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…
We consider the problem of sequential multiple hypothesis testing with nontrivial data collection costs. This problem appears, for example, when conducting biological experiments to identify differentially expressed genes of a disease…
We discuss the use of likelihood asymptotics for inference on risk measures in univariate extreme value problems, focusing on estimation of high quantiles and similar summaries of risk for uncertainty quantification. We study whether…
This article studies tail behavior for the error components in the stochastic frontier model, where one component has bounded support on one side, and the other has unbounded support on both sides. Under weak assumptions on the error…
Let $\alpha_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)$ be the predictive distributions of a sequence $(X_1,X_2,\ldots)$ of $p$-dimensional random vectors. Suppose $$\alpha_n= \mathcal{N} _p (M_n,Q_n)$$ where…
A spectral problem is considered in a thin $3D$ graph-like junction that consists of three thin curvilinear cylinders that are joined through a domain (node) of the diameter $\mathcal{O}(\varepsilon),$ where $\varepsilon$ is a small…
We discuss the asymptotic behaviour of risk-based indifference prices of European contingent claims in discrete-time financial markets under volatility uncertainty as the number of intermediate trading periods tends to infinity. The…
In [16], a new family of vector-valued risk measures called multivariate expectiles is introduced. In this paper, we focus on the asymptotic behavior of these measures in a multivariate regular variations context. For models with equivalent…
We develop an extreme value framework for CoVaR centered on $v(q \mid p ; C)$, the copula-adjusted probability level, or equivalently, the CoVaR on the uniform (0,1) scale. We characterize the possible tail regimes of $v(q \mid p ; C)$…
This paper considers estimation and inference about tail features when the observations beyond some threshold are censored. We first show that ignoring such tail censoring could lead to substantial bias and size distortion, even if the…
In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability $\alpha$, the $100\alpha\%$ VaR is…
This paper considers the question of characterizing the behavior of waves reflected by a fractional singularity of the wave speed profile, i.e., of the form \[ c(x_1, x_2, x_3) = c_0 \left(1 + \left( \frac{x_1}{\ell}\right)_{+}^\alpha…
We analyze the problem of discrete distribution estimation under $\ell_1$ loss. We provide non-asymptotic upper and lower bounds on the maximum risk of the empirical distribution (the maximum likelihood estimator), and the minimax risk in…
In this paper, we investigate risk measures such as value at risk (VaR) and the conditional tail expectation (CTE) of the extreme (maximum and minimum) and the aggregate (total) of two dependent risks. In finance, insurance and the other…
Extreme value theory provides an asymptotically justified framework for estimation of exceedance probabilities in regions where few or no observations are available. For multivariate tail estimation, the strength of extremal dependence is…
We consider a Bayesian problem of estimating of probability of success in a series of conditionally independent trials with binary outcomes. We study the asymptotic behaviour of differential entropy for posterior probability density…
We investigate a multi-factor extension of the asymptotic single risk factor (ASRF) model that underlies the capital charges of the "Basel II Accord". In this extended model, it is still possible to derive closed-form solutions for the risk…