The paper establishes a connection between different risk measures and their risk contributions.
problem Understanding the relationship between conditional coherent and deviation risk measures.
method Axiomatic framework and continuous-time risk contribution analysis.
result Risk contributions of time-consistent risk measures are also time-consistent.
We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional aggregation and a univariate conditional risk measure. Our studies extend known results f…
The paper develops a new approach to conditional risk measures using modular convex analysis.
problem Developing a new method for conditional risk measures.
method Random modular approach to conditional certainty equivalents and niveloids in the conditional L∞-space. result Retrieves a conditional variational formula for optimized certainty equivalents and applies it to the conditional entropic risk measure.
The paper extends static Systemic Risk Measures to a conditional setting.
problem Investigating how static Systemic Risk Measures can be adapted to a conditional framework.
method Providing a general dual representation result, analyzing Conditional Shortfall Systemic Risk Measures, and providing explicit formulas for exponential preferences.
result Explicit formulas for Conditional Shortfall Systemic Risk Measures and a time consistency property.
New risk measures assess cryptocurrency market vulnerabilities during financial distress.
problem Capturing systemic risk in cryptocurrency markets during financial distress.
method Introducing Vulnerability Conditional Risk Measures (VCoES) and related measures.
result Validated theoretical insights and demonstrated practical relevance in cryptocurrency market.
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution (ΔCoD) measures as measures of systemic risk and analyze their properties and representations. The classes include the well-known conditional Value-at-Risk, conditional Expected Shortfall, and r…
New conditional risk measures called conditional generalized quantiles defined and characterized.
problem Developing new risk measures for dynamic risk assessment.
method Propose and characterize conditional generalized quantiles using expected utility model and equivalent conditions.
result Characterized conditional generalized quantiles as well-defined and equivalent to a conditional first order condition.
We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (2016). Further, in analogy to the univariate cas…
To provide a solid analytic foundation for the module approach to conditional risk measures, this paper establishes a complete random convex analysis over random locally convex modules by simultaneously considering the two kinds of topologies (namely the (ε,λ)--topology and the locally L0-- convex topolo…
This paper presents non-parametric estimates of spectral risk measures applied to long and short positions in 5 prominent equity futures contracts. It also compares these to estimates of two popular alternative measures, the Value-at-Risk (VaR) and Expected Shortfall (ES). The spectral risk measures are conditioned on …
This paper deals with multidimensional dynamic risk measures induced by conditional g-expectations. A notion of multidimensional g-expectation is proposed to provide a multidimensional version of nonlinear expectations. By a technical result on explicit expressions for the comparison theorem, uniqueness theorem and…
New financial model revises risk measure under NA condition.
problem Revising classical financial mathematics with coherent risk measure on L0. method Developed a new version of the fundamental theorem of asset pricing and provided dual representations.
result Set of risk-hedging prices is closed under NA condition.
Paper introduces contribution measures for systemic risk in crypto markets.
problem Evaluating systemic risk and quantifying risk interactions in cryptocurrency markets.
method Develops various contribution ratio measures based on MCoVaR, MCoES, and MMME.
result Establishes sufficient conditions for comparing contribution measures between sets of random vectors.
The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a brief introduction to random metric theory, risk measures and conditional risk measu…
Simple conditions for comonotonic additive risk measures from acceptance sets.
problem Conditions for comonotonic additive risk measures from acceptance sets.
method Conditions on acceptance sets for induced comonotonic additive risk measures.
result Acceptance sets induce comonotonic additive risk measures if and only if the acceptance sets and their complements are stable under convex combinations of comonotonic random variables.
We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no-arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized …
Investigates conditional Chisini means and their application to risk measures.
problem Existence of conditional nonlinear means for bounded random variables.
method Defines a mean as a solution to a functional equation induced by T, and provides conditions for the existence of a unique solution.
result Characterizes the scalarization of conditional Risk Measures.
New framework for calculating multivariate risk measures using Wishart process.
problem Quantifying multivariate risk measures in financial markets.
method Introducing a new analytical framework based on the Wishart process.
result Explicit computation of conditional tail risk measures up to two dimensions.
This paper applies an AR(1)-GARCH (1, 1) process to detail the conditional distributions of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses the conditional distribution for these contracts to estimate spectral risk measures, which are coherent risk measures …
New vine copula method forecasts portfolio risk measures robust to market downturns.
problem Inaccurate risk measure estimation for financial portfolios due to lack of cross-dependency capture.
method Combines vine copulas with ARMA-GARCH models for marginal risk estimation.
result Portfolio is robust to American market downturns but not European market.
Paper discusses natural quasiconvexity and its relation to decomposable sums in risk measures.
problem Understanding natural quasiconvexity and its implications in risk measures.
method Relates natural quasiconvexity to decomposable sums, proposes a general treatment of convexity index, and proves equivalence for certain spaces.
result Natural quasiconvexity and convexity are equivalent for conditional risk measures on Lp spaces under mild conditions. Paper introduces DCoVaR for aggregate risk models, outperforming existing methods.
problem Lack of coherent risk measures for aggregate risk models.
method Proposes Dependent Conditional Value-at-Risk (DCoVaR) for a target loss dependent on another random loss.
result DCoVaR outperforms MCoVaR and CCoVaR in numerical simulations and empirical studies.
The paper derives risk measures for metalog distributions.
problem Deriving risk measures for metalog distributions.
method Closed-form expressions for Conditional Value at Risk and first-order partial moments.
result First-order partial moments are convex with respect to metalog parameters.
Dynamic risk measures follow law invariance principles over time.
problem Tackles dynamic risk measurement principles.
method Shows equivalence between adapted law invariance and recursive one-step conditional-law representation for time-consistent risk measures.
result Identifies adapted law invariance as the dynamic counterpart of ordinary law invariance.
In this paper we study the effect of network structure between agents and objects on measures for systemic risk. We model the influence of sharing large exogeneous losses to the financial or (re)insuance market by a bipartite graph. Using Pareto-tailed losses and multivariate regular variation we obtain asymptotic resu…
Working in a continuous time setting, we extend to the general case of dynamic risk measures continuous from above the characterization of time consistency in terms of ``cocycle condition'' of the minimal penalty function. We prove also the supermartingale property for general time consistent dynamic risk measures. Whe…
Unified asymptotic treatment for VaR- and expectile-based systemic risk measures.
problem Analyzing systemic risk measures under extreme system-wide disasters.
method Classified systemic risk measures into VaR- and expectile-based families, introduced new ICE and SICE measures, and provided second-order asymptotic results.
result Second-order asymptotics provide more accurate tail approximations for systemic risk measures.
A new framework for robust risk measurement and portfolio optimization.
problem Uncertainty in mean-covariance space and portfolio optimization challenges.
method Modeling uncertainty with Gelbrich distance and prior structural information, related to optimal transport theory.
result Mean-covariance robust portfolio optimization simplifies to Markowitz model with a regularization term.
This paper compares two different frameworks recently introduced in the literature for measuring risk in a multi-period setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, while the second involves applying a composition of one-step coherent risk mappings. We summar…
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 consistency properties of dynamic risk measures in terms of acceptance sets, penalty …
Our goal in this paper is to propose an alternative risk measure which takes into account the fluctuations of losses and possible correlations between random variables. This new notion of risk measures, that we call Copula Conditional Tail Expectation describes the expected amount of risk that can be experienced given …
Paper develops NPG for risk-averse RL with ECRMs, proving global convergence.
problem Ensuring reliable performance in stochastic RL problems with risk-averse policies.
method Developed natural policy gradient updates for ECRMs-based RL problems, proving global optimality and iteration complexity.
result Global convergence of risk-averse NPG algorithm with ECRMs.
This paper connects monetary and star-shaped risk measures by showing their equivalence under certain conditions.
problem Understanding the relationship between monetary and star-shaped risk measures.
method Analyzing the acceptability of 0 and the normalization property.
result Monetary risk measures are only a translation away from star-shapedness under mild conditions.
Paper proposes a new method to evaluate joint risk under uncertainty.
problem Evaluating joint risk of multiple insurance risks under dependence uncertainty.
method Axiomatic approach to scalar and vector-valued distortion joint risk measures.
result Established a new scalar distortion joint risk measure with positive homogeneity.
This paper introduces a new systemic risk measure, JMES, and its associated contribution measures.
problem Measuring systemic risk and its contributions among entities.
method Proposes JMES and associated contribution measures, studies their properties, and compares them with existing measures.
result Established sufficient conditions for comparing JMES and other measures under different copula structures and stress levels.
Enhances resilience evaluation by using dynamic convex risk measures.
problem Capturing the full risk profile of financial positions under adverse conditions.
method Introduces a new resilience evaluation method using dynamic convex risk measures.
result Shows that the resilience evaluation can distinguish between positions with the same expected recovery but different conditional risk profiles.
Develops a new risk measure for Markov chains' asymptotic behavior.
problem Lack of risk measures for asymptotic regimes of Markov chains.
method Simulation-based approach using large deviations theory, density estimation, and stochastic approximation.
result Developed Asymptotic CVaR (ACVaR) for Markov chains.
The study proposes a method for risk reduction without relying on risk measurement.
problem Theoretical utopia of risk minimization vs. practical risk reduction.
method Generalization of matrix rank and condition number for identifying riskiest scenarios.
result Risk reduction achieved without risk measurement, validated by real data.
Establishes a link between risk measures and uniform integrability in finance.
problem Understanding uniform integrability in the context of financial risk measures.
method Introduces the folding score of distortion risk measures to study uniform integrability directly with gains and losses.
result Obtains three sets of equivalent conditions for uniform integrability involving coherent risk measures.
Proposes a new risk measurement method for risk-averse stochastic optimization.
problem Risk-averse stochastic optimization problems.
method Develops a risk measure based on argmin and minimum concepts.
result Guarantees the existence of solutions for the proposed problem.
In this paper we look at the efficacy of different risk measures on energy markets and across several different stock market indices. We use both the Value at Risk and the Tail Conditional Expectation on each of these data sets. We also consider several different durations and levels for historical risk measures. Throu…
This paper shows how to calculate risk measures for sums of two counter-monotonic risks.
problem Calculating risk measures for sums of two counter-monotonic risks.
method Using a fixed distortion function and expressing the risk measure of a sum as the sum of two related measures of the marginals.
result The risk measure of a sum of two counter-monotonic risks can be expressed as the sum of two related distortion risk measures of the marginals.
This paper was presented and written for two seminars: a national UK University Risk Conference and a Risk Management industry workshop. The target audience is therefore a cross section of Academics and industry professionals. The current ongoing global credit crunch has highlighted the importance of risk measurement i…
We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and certainty equivalent to conditional acceptability indexes. We provide the characteriza…
We estimate risk measures in Markov cost processes with lower and upper bounds.
problem Estimating risk measures in infinite-horizon discounted costs within Markov processes.
method Truncation scheme and lower/upper bounds for CVaR and variance estimation.
result Upper and lower bounds for CVaR and variance estimation match up to logarithmic factors.
Paper introduces TVaRD, a new topological risk measure for financial portfolios.
problem Traditional risk measures like VaR and CVaR are insufficient for complex market conditions.
method Topological data analysis (TDA) using cohomology groups on financial time series data.
result TVaRD reveals significant changes in financial time series during stress conditions.
Study systemic risk measures adjusted to financial markets.
problem Systemic risk in financial systems with market adjustments.
method Dual representation for convex robust systemic risk measures adjusted to the financial market.
result Relation to no-arbitrage conditions.
Derives derivatives of risk measures for various types of portfolio losses.
problem Calculating precise risk measures for portfolio losses.
method Analyzes first and second order derivatives of risk measures for both continuous and discrete portfolio loss scenarios.
result Provides asymptotic results for conditional moments of heavy-tailed portfolio losses.