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.
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.
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 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.
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.
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.
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.
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.
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.
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.
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.
A new tail-shape index based on Value at Risk and Expected Shortfall.
problem Measuring and comparing tail behavior of loss distributions.
method Introducing a new θ-index based on equal level relationships between Value at Risk and Expected Shortfall. result The θ-index provides a level-dependent, scale-free measure of upper tail behavior. We present a method of hedging Conditional Value at Risk of a position in stock using put options. The result leads to a linear programming problem that can be solved to optimise risk hedging.
Deep neural networks reduce loan portfolio risk.
problem Minimizing risk in peer-to-peer lending portfolios.
method Proposed DeNN and DSNN models to predict default probability and time.
result DeNN model significantly reduces portfolio VaRs at various confidence levels.
Study improves accuracy of risk measures using advanced algorithms.
problem Computing accurate risk measures for financial losses.
method Nested stochastic approximation and multilevel acceleration.
result Established central limit theorems for estimation errors.
Quantification of risk positions under model uncertainty is of crucial importance from both viewpoints of external regulation and internal management. The concept of model uncertainty, sometimes also referred to as model ambiguity. Although we know the family of models, we cannot precisely decide which one to use. Give…
Improved multilevel scheme for value-at-risk computation.
problem Discontinuity in Heaviside function affects value-at-risk computation.
method Adaptive multilevel stochastic approximation to mitigate discontinuity.
result Best complexity improved to O(ε−2∣lnε∣25). 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.
We tackle imbalanced classification by weighting losses and derive robust risks.
problem Imbalanced classification where a label has low marginal probability.
method We examine convergence rates of weighted risks, define robust risks, and derive new robust risk problems.
result We show that particular weightings lead to conditional value at risk (CVaR) and derive new robust risk problems.
Quantum method calculates risk contributions in credit portfolios efficiently.
problem Quantifying risk concentration in subgroups of a credit portfolio.
method Quantum algorithm for simultaneous estimation of multiple expected values.
result Quantum method scales better than classical methods for finely divided subgroups.
In this paper we propose a novel Bayesian methodology for Value-at-Risk computation based on parametric Product Partition Models. Value-at-Risk is a standard tool to measure and control the market risk of an asset or a portfolio, and it is also required for regulatory purposes. Its popularity is partly due to the fact …
The paper mentioned in the title introduces the entropic value at risk. I give some extra comments and using the general theory make a relation with some commonotone risk measures.
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.
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.
Paper investigates Lambda Value-at-Risk under ambiguity and risk sharing.
problem Investigates Lambda Value-at-Risk under ambiguity and risk sharing.
method Establishes equivalence of robust ΛVaR and traditional ΛVaR under ambiguity sets, analyzes properties, derives explicit formulas, and explores risk sharing. result Unified and extended the concept of Value-at-Risk under ambiguity, derived explicit formulas for specific ambiguity sets, and explored risk sharing.
New model uses interval-valued CVaR for better risk assessment in finance.
problem Measuring tail risk in rapidly changing financial markets.
method Employing random intervals to describe asset returns and using ICVaR as a risk measure.
result Optimal portfolio selection models show better risk assessment in real data.
In the paper, we use and investigate copulas models to represent multivariate dependence in financial time series. We propose the algorithm of risk measure computation using copula models. Using the optimal mean-CVaR portfolio we compute portfolio's Profit and Loss series and corresponded risk measures curves. Value-…
Researchers calculated EVaR for various distributions using Lambert function.
problem Difficulty in finding analytical representation of EVaR measure.
method Used Lambert function to calculate EVaR for multiple distributions.
result Successfully calculated EVaR for 7 specific distributions.
New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first "regulator" version is independent from any market model whereas the second version, called the market extension, takes trading …
In this paper, we generalize the parametric delta-VaR method from portfolios with normally distributed risk factors to portfolios with elliptically distributed ones. We treat both the expected shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of a multivariate t-distr…
Paper presents efficient IS for tail risk estimation with machine learning features.
problem Estimating Value at Risk and Conditional Value at Risk with black-box access.
method Efficient Importance Sampling algorithm with self-structuring transformation.
result Asymptotically optimal variance reduction in logarithmic scale.
This paper analyzes risk-sensitive reinforcement learning with Conditional Value-at-Risk (CVaR) for robust Markov Decision Processes.
problem Risk-sensitive reinforcement learning for robust Markov Decision Processes (RMDPs) with state-action-dependent ambiguity sets.
method The paper establishes a connection between robustness and risk sensitivity, defining a new risk measure NCVaR and proposing value iteration algorithms.
result The proposed approach using NCVaR optimization and value iteration algorithms can solve problems with state-action-dependent ambiguity sets.
In this study, we propose a new definition of multivariate conditional value-at-risk (MCVaR) as a set of vectors for discrete probability spaces. We explore the properties of the vector-valued MCVaR (VMCVaR) and show the advantages of VMCVaR over the existing definitions given for continuous random variables when adapt…
This paper presents analytical solutions to the problem of how to calculate sensible VaR (Value-at-Risk) and ES (Expected Shortfall) contributions in the CreditRisk+ methodology. Via the ES contributions, ES itself can be exactly computed in finitely many steps. The methods are illustrated by numerical examples.
Study tail behavior of sum of heavy-tailed risks with copulas.
problem Analyzing the tail behavior of sums of heavy-tailed risks with dependence modeled by copulas.
method Modeling dependence with copulas and analyzing tail asymptotics of sums of heavy-tailed risks.
result Obtained asymptotic expansions for Value-at-Risk of aggregate risk.
Value-at-Risk (VaR) is an institutional measure of risk favored by financial regulators. VaR may be interpreted as a quantile of future portfolio values conditional on the information available, where the most common quantile used is 95%. Here we demonstrate Conditional Autoregressive Value at Risk, first introduced by…
Numerical challenges inherent in algorithms for computing worst Value-at-Risk in homogeneous portfolios are identified and solutions as well as words of warning concerning their implementation are provided. Furthermore, both conceptual and computational improvements to the Rearrangement Algorithm for approximating wors…
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…
EX-DRL improves extreme quantile prediction for financial risk management.
problem Inaccurate estimation of extreme quantiles in loss distributions.
method EX-DRL uses Generalized Pareto Distribution (GPD) to model the tail of the loss distribution and Quantile Regression (QR) to improve extreme quantile prediction.
result EX-DRL provides more precise estimates of extreme quantiles, improving risk metrics reliability.
Paper improves VaR risk allocation by avoiding zero probability events.
problem Computing VaR contributions for zero probability events.
method Reformulates Euler contributions to a ratio of conditional expectations with strictly positive probability events.
result Proposed estimator outperforms standard Monte Carlo methods in bias and variance.
The objective in a traditional reinforcement learning (RL) problem is to find a policy that optimizes the expected value of a performance metric such as the infinite-horizon cumulative discounted or long-run average cost/reward. In practice, optimizing the expected value alone may not be satisfactory, in that it may be…