Related papers: Conditional Value at Risk and Partial Moments for …
Many key quantities in statistics and probability theory such as the expectation, quantiles, expectiles and many risk measures are law-determined maps from a space of random variables to the reals. We call such a law-determined map, which…
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes…
Our paper contributes to the theory of conditional risk measures and conditional certainty equivalents. We adopt a random modular approach which proved to be effective in the study of modular convex analysis and conditional risk measures.…
Expectile, as the minimizer of an asymmetric quadratic loss function, is a coherent risk measure and is helpful to use more information about the distribution of the considered risk. In this paper, we propose a new risk measure by replacing…
For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random…
Gaussian random vectors exhibit the loss of dimension phenomena, which relate to their joint survival tail behaviour. Besides, the fact that the components of such vectors are light-tailed complicates the approximations of various…
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…
In risk theory, financial asset returns often follow heavy-tailed distributions. Investors and risk managers used to compare risk measures as the value at risk or tail value at risk in order over the whole confidence levels to avoid the…
This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time…
Optimization of conditional convex risk measure is a central theme in dynamic portfolio selection theory, which has not yet systematically studied in the previous literature perhaps since conditional convex risk measures are neither random…
This paper approaches the definition and properties of dynamic convex risk measures through the notion of a family of concave valuation operators satisfying certain simple and credible axioms. Exploring these in the simplest context of a…
Conditional Monte Carlo refers to sampling from the conditional distribution of a random vector X given the value T(X) = t for a function T(X). Classical conditional Monte Carlo methods were designed for estimating conditional expectations…
An equational axiomatisation of probability functions for one-dimensional event spaces in the language of signed meadows is expanded with conditional values. Conditional values constitute a so-called signed vector meadow. In the presence of…
The paper derives saddlepoint expansions for conditional expectations in the form of $\mathsf{E}[\overline{X} | \overline{\mathbf Y} = {\mathbf a}]$ and $\mathsf{E}[\overline{X} | \overline{\mathbf Y} \geq {\mathbf a}]$ for the sample mean…
We study the variability of a risk from the statistical viewpoint of multimodality of the conditional loss distribution given that the aggregate loss equals an exogenously provided capital. This conditional distribution serves as a building…
In this paper we provide a new criterion for the comparison of claims, when we have conditional claims arising in stop loss contracts or contracts with franchise deductible. These stochastic comparisons are made on the basis of the Tail…
This paper investigates the asymptotic behavior of higher-order conditional tail moments, which quantify the contribution of individual losses in the event of systemic collapse. The study is conducted within a framework comprising two…
We present the conditional value-at-risk (CVaR) in the context of Markov chains and Markov decision processes with reachability and mean-payoff objectives. CVaR quantifies risk by means of the expectation of the worst p-quantile. As such it…
This paper is organized in three parts closely related to closure properties of heavy-tailed distributions and heavy-tailed random vectors. In the first part we consider two random variables X and Y with distributions F and G respectively.…
Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional…