Extended univariate Range Value-at-Risk to multivariate settings.
problem Inability of traditional risk measures for heavy-tail distributions and infinite tail expectations.
method Multivariate definitions of robust truncated tail expectations, robustness and properties derived, closed-form expressions and special cases discussed.
result Empirical estimators accuracy examined through numerical and graphical examples.
The paper introduces MRVaR and MRCov for elliptical and log-elliptical distributions.
problem Risk management of regulation and investment purposes.
method Proposes MRVaR and MRCov as risk measures for elliptical and log-elliptical distributions.
result Explicit expressions of MRVaR and MRCov derived for multivariate (log-)elliptical distributions.
Paper quantifies distortion risk measures' robustness to distributional uncertainty.
problem Quantifying risk measures' robustness to distributional uncertainty.
method Employing isotonic projections, the paper derives bounds on distortion risk measures' values.
result Sharp bounds on distortion risk measures' values are provided, especially for Value-at-Risk and Range-Value-at-Risk.
Study extreme-case Value-at-Risk under IFR distributions, providing guidance for risk management.
problem Understanding extreme-case risk measures under distributional ambiguity and increasing failure rate.
method Characterized extreme-case range Value-at-Risk under mean and variance constraints with increasing failure rate.
result Characterized specific characteristics of extreme-case distributions under IFR constraints.
This paper evaluates Range Value at Risk forecasts using consistent scoring functions.
problem Evaluating and comparing the performance of Range Value at Risk (RVaR) forecasts.
method Using strictly consistent loss or scoring functions, the paper characterizes the class of scoring functions for a triplet of RVaR with two VaR components.
result A triplet of RVaR with two VaR components at different levels is elicitable, and the class of strictly consistent scoring functions is characterized.
In this paper we consider reinsurance or risk sharing from a macroeconomic point of view. Our aim is to find socially optimal reinsurance treaties. In our setting we assume that there are n insurance companies each bearing a certain risk and one representative reinsurer. The optimization problem is to minimize the su…
This paper calculates worst-case VaR for financial markets using empirical data and model uncertainty.
problem Quantifying risk under model uncertainty for financial risk management.
method Proposed a two-layer mixed distribution model to simplify model uncertainty, used change point detection and EM algorithm for estimation.
result Calculated VaR, WVaR, and BVaR for four financial markets, analyzed their performance.
Paper provides new bounds for risk aggregation and sharing.
problem Quantitative risk management and robust risk aggregation with dependence uncertainty.
method Established new inequality for RVaR, derived extended convolution bounds, and analyzed risk sharing for averaged quantiles.
result Extended convolution bounds for robust risk aggregation and risk sharing, providing sharpness conditions and explicit expressions.
Bayesian realized EGARCH models improve tail risk forecasting.
problem Forecasting tail risks in financial markets.
method Developed a Bayesian framework for realized EGARCH models, incorporating multiple realized volatility measures and using robust adaptive Metropolis algorithm for estimation.
result Standardized skewed Student-t distribution and sub-sampled realized range models outperform other models in tail risk forecasting.
Sharp bounds for distortion risk metrics under uncertain distributions.
problem Modeling risk metrics under distributional uncertainty.
method Established bounds for distortion risk metrics using specific features of underlying distributions.
result Identified worst- and best-case values of distortion risk metrics.
We use a replica approach to deal with portfolio optimization problems. A given risk measure is minimized using empirical estimates of asset values correlations. We study the phase transition which happens when the time series is too short with respect to the size of the portfolio. We also study the noise sensitivity o…
A new realized conditional autoregressive Value-at-Risk (VaR) framework is proposed, through incorporating a measurement equation into the original quantile regression model. The framework is further extended by employing various Expected Shortfall (ES) components, to jointly estimate and forecast VaR and ES. The measu…
The joint Value at Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2017) is extended via incorporating a realized measure, to drive the tail risk dynamics, as a potentially more efficient driver than daily returns. Both a maximum likelihood and an adaptive Bayesian Markov Chain Monte Carlo m…
The paper optimizes reinsurance under uncertain dependence among insurers.
problem Designing Pareto-optimal reinsurance contracts in a market with uncertain dependence.
method Robust optimization approach assuming known marginal distributions and unspecified dependence structure.
result Characterization of optimal indemnity schedules under worst-case scenario and derivation of optimal two-parameter layer contracts for independent risks.
Paper establishes identifiability and elicitability of tail risk measures.
problem Identifying and measuring tail risk measures accurately.
method Establishes identifiability and elicitability of tail risk measures using generators and quantiles.
result Joint identifiability and elicitability of tail risk measures and quantiles.
We study capital requirements for bounded financial positions defined as the minimum amount of capital to invest in a chosen eligible asset targeting a pre-specified acceptability test. We allow for general acceptance sets and general eligible assets, including defaultable bonds. Since the payoff of these assets is not…
The study evaluates the performance of ANNs in financial forecasting.
problem Mixed evidence on the predictive performance of ANNs for financial time-series data.
method Proposes a flexible nonparametric model and compares its performance to other estimators.
result The proposed model shows better performance than basic benchmarks in estimating Value-at-Risk.
Bayesian LSTM model improves VaR and ES forecasting accuracy.
problem Joint forecasting of Value at Risk (VaR) and Expected Shortfall (ES).
method Hybrid model combining LSTM for time series dynamics and Asymmetric Laplace quasi-likelihood for joint likelihood.
result The LSTM-AL model outperforms existing models in VaR and ES forecasting accuracy.
In this paper we discuss a general methodology to compute the market risk measure over long time horizons and at extreme percentiles, which are the typical conditions needed for estimating Economic Capital. The proposed approach extends the usual market-risk measure, ie, Value-at-Risk (VaR) at a short-term horizon and …
Investors optimize their portfolios within a Wasserstein ball to match a benchmark's risk profile.
problem Optimizing portfolio performance while maintaining risk proximity to a benchmark.
method Optimal dynamic strategy selection based on minimizing distortion risk measures within a Wasserstein ball.
result An optimal dynamic strategy exists and can be calculated through isotonic projections.
The paper shows vector-valued risk measures ignore dependence structures.
problem Defining capital allocation rules for random vectors with dependence.
method Defined vector-valued risk measures by axioms and showed their properties.
result Vector-valued risk measures ignore dependence structures, unlike set-valued measures.
This research improves value-at-risk estimation during financial crises using non-extensive statistical methods.
problem Underestimation of value-at-risk during financial crises.
method Non-extensive value-at-risk model based on Tsallis entropy and q-Gaussian probability density function.
result The q-Gaussian model provides better value-at-risk estimation during financial crises.
A new model forecasts financial risks using multiple realized measures.
problem Forecasting financial risks using multiple realized measures.
method Developed a semi-parametric joint VaR and ES forecasting framework using realized measures.
result The proposed model outperformed other models in forecasting financial risks.
Hybrid GARCH-GRU model improves volatility forecasting for financial assets.
problem Improving volatility and risk forecasting for financial assets.
method Combining GARCH models with GRU neural networks.
result Hybrid models produce more accurate volatility forecasts.
Approximate Incremental Value-at-Risk formulae provide an easy-to-use preliminary guideline for risk allocation. Both the cases of risk adding and risk pooling are examined and beta-based formulae achieved. Results highlight how much the conditions for adding new risky positions are stronger than those required for ris…
Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function mapping random variables to the real numbers. Nowadays "value-at-risk", which is d…
Study risk sharing with Lambda VaR under diverse beliefs.
problem Risk sharing among agents with different beliefs.
method Use Lambda Value-at-Risk as preference, analyze under heterogeneous beliefs.
result Explicit formulas for risk sharing under various belief scenarios.
New risk measure includes VaR, TVaR, and Entropic Risk Measure.
problem Risk management with specific focus on tail risk.
method Generalized Quasi-Linear Means restricted to the tail of the risk distribution.
result Unified measure for VaR, TVaR, and Entropic Risk Measure.
Researchers extend CCVaR to multivariate data using Archimedean copulas.
problem No multivariate extension for CCVaR when dependence is given by Archimedean copulas.
method Derive an almost closed-form expression for CCVaR under an Archimedean copula, examine coherence conditions, and conduct numerical experiments.
result An almost closed-form expression for CCVaR under an Archimedean copula is derived.
Study examines cryptocurrency impacts on financial indices using advanced risk models.
problem Interdependence between cryptocurrencies and financial indices, focusing on risk spillover.
method Hybrid approach integrating GARCH, EVT, and copula functions for risk measures.
result eGARCH-EVT-Copula model outperforms conventional methods in risk estimation.
Study optimal portfolio selection with Recovery Average Value at Risk, showing better control over liabilities.
problem Optimizing portfolios with a new risk measure under known or uncertain distributions.
method Existence results for mean-risk optimal portfolios under different distributional assumptions.
result Portfolio selection under Recovery Average Value at Risk provides better control over liabilities.
New model incorporates long-range dependence in mortality rates for better valuation and risk management.
problem Lack of appropriate models for valuing and managing mortality securities with long-range dependence.
method Proposes a novel class of Volterra mortality models that incorporate LRD, derived in closed-form solution.
result Models provide flexibility and tractability for valuing and hedging mortality-related products.
In this paper, we propose a novel investment strategy for portfolio optimization problems. The proposed strategy maximizes the expected portfolio value bounded within a targeted range, composed of a conservative lower target representing a need for capital protection and a desired upper target representing an investmen…
The paper analyzes how to combine self-protection and self-insurance for risk reduction.
problem Combining self-protection and self-insurance for risk reduction when market insurance is absent.
method The approach uses Value-at-Risk and Tail Value-at-Risk to evaluate residual risk and solves the problem using isoquant geometry based on marginal-balance curves.
result The analysis identifies the conditions under which self-protection and self-insurance behave as substitutes or complements.
Quantum SVT reduces credit risk analysis costs.
problem Efficiently estimating credit risk metrics using quantum computing.
method Quantum Singular Value Transformation (QSVT) to reduce state preparation costs.
result Significant reduction in implementation costs for quantum credit risk analysis.
Value-at-Risk is a flawed substitute for non-ruin capital, leading to misleading financial standards.
problem Misuse of Value-at-Risk as a risk measure, replacing non-ruin capital, leads to flawed financial standards.
method Mathematical analysis of risk measures and their implications on financial standards.
result Non-ruin capital is a more accurate risk measure than Value-at-Risk, necessitating its adoption over the former.
Paper compares LSTM and GARCH for estimating value-at-risk.
problem Estimating value-at-risk on time series with heteroscedastic dynamics.
method Uses LSTM neural networks to estimate value-at-risk compared to GARCH benchmarks.
result LSTM outperforms GARCH on real market data in terms of exception rate and mean quantile score.
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.
Paper optimizes liquidity provision in decentralized finance markets.
problem Strategic LPs face predictable losses and concentration risk in CL pools.
method Derive optimal liquidity provision strategy based on fees, PL, and concentration risk.
result Optimal strategy increases fee revenue and profit from marginal rate changes.
CGAN simulates time series data using categorical and continuous auxiliary info.
problem Simulating time series data with conditional information.
method Conditional Generative Adversarial Net (CGAN) for learning and generating time series data.
result CGAN can learn and generate various time series distributions and structures.
Classifies financial risk into three levels based on first passage times.
problem Modeling financial risk under varying conditions with time-varying thresholds.
method Qualitative classification into high, medium, and low risk categories based on first passage time behavior.
result A three-level classification of risk based on the asymptotic behavior of the default function.
New risk measure improves creditor protection in financial regulation.
problem Current solvency requirements fail to control the size of recovery on creditors' claims.
method Developed Recovery Value at Risk (Recovery VaR) to control recovery on creditors' claims.
result Recovery VaR flexibly controls recovery on creditors' claims and integrates protection needs into management incentives.
New property shows VaR subadditivity for comonotonic loss variables.
problem Understanding VaR subadditivity and comonotonicity.
method Analyzes VaR subadditivity and comonotonicity relationship.
result VaR subadditivity holds for comonotonic loss variables.
The paper analyzes the risk of investing in a basket of 27 cryptocurrencies using statistical distributions.
problem Risk assessment of capital allocation in a basket of cryptocurrencies.
method Used statistical tests to determine the most appropriate distribution (SDI) for modeling returns, and adapted the generalized Pareto distribution for tail risk assessment.
result Found that a combination of stable and generalized Pareto distributions provides a more accurate risk assessment for the basket of cryptocurrencies.
A new method forecasts financial tail risks by combining and weighting quantiles.
problem Reducing uncertainty in financial tail risk forecasting.
method Two-step procedure: quantile combination followed by ES computation.
result The proposed framework outperforms individual models and simple approaches.
Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile regression applied to the tails, is of interest in many economic and financial applicat…
Enhances Transformers for better risk assessment in finance.
problem Transformer models lack sensitivity to extreme financial losses.
method Integrates Loss-at-Risk function with Value at Risk (VaR) and Conditional Value at Risk (CVaR).
result Improves risk prediction and management in financial datasets.
We propose a modified time lag random matrix theory in order to study time lag cross-correlations in multiple time series. We apply the method to 48 world indices, one for each of 48 different countries. We find long-range power-law cross-correlations in the absolute values of returns that quantify risk, and find that …