This paper uses information theory to improve risk modeling in big data.
problem Insufficient application of information theory in actuarial science.
method Explores information theory to uncover performance limits of insurance big data systems.
result Guidance for risk modeling and actuarial pricing systems.
Develops a statistical framework for coherent risk estimation.
problem Constructing coherent risk estimators with sound financial and statistical properties.
method Inspired by axiomatic risk measure theory, defines coherent risk estimators through robust representations linked to L-estimators. result Demonstrates that coherence of a risk measure does not necessarily carry over to its estimators and shows alternative weight structures can lead to different outcomes.
The paper tackles catastrophic risk in reinforcement learning using extreme value theory.
problem Mitigating catastrophic risk in sequential decision making with limited observations.
method Developed POTPG, a policy gradient algorithm based on extreme value theory.
result POTPG outperforms common benchmarks in numerical experiments.
New concept of partial law invariance connects decision theory and financial risk management.
problem Connecting decision theory and financial risk management under uncertainty.
method Characterizing partially law-invariant coherent risk measures via a novel representation formula.
result Strong partial law invariance bridges the gap between existing risk measure representations.
A novel model combines deep learning and extreme value theory for multivariate cyber risk prediction.
problem High dimensionality and heavy tails in multivariate cyber risk patterns.
method Combines deep learning for point predictions and extreme value theory for quantile predictions.
result The model provides satisfactory high quantile predictions and accurate point predictions.
The paper examines the feasibility of managing aggregate cyber-risk in IoT environments.
problem Determining sustainable conditions for providing aggregate cyber-risk coverage.
method Developed a rigorous general theory and validated it with real data.
result Conditions for sustainable aggregate cyber-risk management under heavy-tailed distributions.
Network theory assesses systemic risk in the insurance sector.
problem Detecting critical insurance companies in systemic risk.
method Complex network approach with weighted effective resistance centrality.
result Identifies companies with significant influence on network robustness.
New risk theory for 'Pay-for-Performance' models.
problem How to price and hedge operational and financial risks in new business models.
method Developed a new risk theory and calculation method for 'Pay-for-Performance' models.
result Presented a model for determining risk premiums including both financial and operational risks.
The Shapley value theory is used for risk allocation in non-orthogonal risk factors.
problem Risk allocation among non-orthogonal risk factors in financial portfolios.
method Using Shapley value from cooperative game theory to allocate risk contributions.
result Explicit formulas and numerical algorithms for calculating risk allocations are derived.
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.
Paper explores how risk-averse individuals' willingness to pay for insurance varies with risk probability.
problem Understanding how risk-averse individuals' willingness to pay for insurance varies with risk probability.
method Analyzes willingness to pay (WTP) for partial risk reduction within the dual theory of decision.
result In dual theory, reducing the probability of risk and providing insurance can be complementary if the surplus increases with risk reduction.
Study asymptotic properties of generalized shortfall risk measures for heavy-tailed risks.
problem Understanding risk measures for heavy-tailed risks.
method Derive asymptotic expansions for generalized shortfall risk measures.
result Unified theory for risk measures including distortion and utility-based measures.
Introduces an unobservable intrinsic electricity price to link storage theory with risk premium.
problem Connecting storage theory with risk premium in electricity markets.
method Introduces an unobservable intrinsic electricity price and derives prices for various contracts.
result Finds an overall negative risk premium in empirical analysis.
This study proves new financial market theorems breaking standard risk definitions.
problem Breaking standard risk definitions in financial markets.
method Presenting proofs for new financial market theorems.
result New definitions are richer and broader than standard ones considering shape.
The work deals with the risk assessment theory. An unitary risk algorithm is elaborated. The algorithm is based on parallel curves. The basic curve of risk is a hyperbolic curve, obtained as a multiplication between the probability of occurrence of certain event and its impact. Section 1 contains the problem formulatio…
This paper uses MIS to identify key financial institutions with minimal risk contagion.
problem Mitigating systemic risk during extreme financial events.
method Applying extreme value theory and MIS from graph theory to identify diversified portfolios.
result Identified a subset of institutions with minimal extremal dependence for diversified portfolios.
The paper finds stocks with higher dynamic network risk have lower returns.
problem Understanding and pricing short-term and long-term dynamic network risk in stock returns.
method Examined the relationship between stock sensitivities to dynamic network risk and expected returns, using economic theory and empirical analysis.
result A one-standard deviation increase in long-term network risk loadings associates with a 7.66% drop in annualized expected returns.
Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.
problem Capturing higher-order tail behavior and dependence effects in risk measures.
method Second-order asymptotic expansions using extreme value theory and regular variation theory.
result Second-order approximations reduce approximation errors, especially at extreme confidence levels.
Study on test risk dynamics in learning theory with stochastic gradient flow.
problem Understanding test risk in stochastic gradient flow dynamics.
method Path integral formulation for small learning rates, explicit computation for weak features.
result Explicit corrections due to stochastic term in dynamics, good agreement with simulations.
Paper introduces a new method for allocating capital based on risk measures from ruin theory.
problem Allocating capital to manage risk measures derived from ruin theory.
method Introduces a novel allocation method for dynamic value-at-risk (VaR) measures.
result Demonstrates desirable properties and compares with existing methods.
Proposes a network-based strategy to manage financial market risks.
problem Managing extreme events in volatile financial markets.
method Extreme value theory, network model, maximum independent set, value at risk, expected shortfall.
result Developed portfolio strategies improve risk diversification.
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.
A Nash game theory approach allocates capital requirements among financial institutions.
problem Allocating systemic risk measures among financial institutions.
method Proposes a Nash allocation rule inspired by game theory.
result Provides sufficient conditions for the existence and uniqueness of Nash allocation rules.
Paper improves risk estimation for extreme events.
problem Estimating extreme risks accurately.
method Modified Bayes risk for expectiles, asymptotic expansions, efficient estimators.
result Asymptotic normality of estimators proved.
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…
Reply to Tetlock et al. on tail risk and probability gap.
problem Expert judgment fails to account for tail risk.
method Comparison of forecasting tournaments and extreme value theory.
result Greater gap between tail expectation and probability properties.
A framework for anonymized risk sharing without revealing identities or preferences.
problem Risk sharing without revealing individual identities or preferences.
method Axiomatic framework with four key axioms: actuarial fairness, risk fairness, risk anonymity, and operational anonymity.
result The conditional mean risk sharing rule is uniquely characterized by these axioms.
Investigates how diversification preferences relate to risk attitudes.
problem Connecting diversification preferences to risk attitudes.
method Analyzes diversification preferences for various pairs of risks under different conditions.
result Diversification preferences for certain pairs of risks imply specific levels of risk aversion.
This paper compares modern portfolio theories and applies them to real-world portfolio selection.
problem Balancing risk and return in financial investments.
method Introduction of Markowitz's MPT and Fernholz's SPT, application of four models (Markowitz, Constant Correlation, Single Index, Multi-Factor), and use of Portfolio Algorithm and time series models for prediction.
result Comparison and evaluation of portfolio performance and risk management strategies.
Overview of risk-sensitive Markov decision processes with Optimized Certainty Equivalent.
problem Optimizing decision-making under risk in Markov processes.
method Analyzes risk-sensitive criteria using Optimized Certainty Equivalent, including entropic risk and Conditional Value-at-Risk.
result Conditions for the existence of optimal policies and solution procedures are provided.
New theory extends rank-dependent utility for risk and ambiguity.
problem Modeling decision-making under risk and ambiguity.
method Axiomatizes a new preference relation with ambiguity index, probability weighting, and utility function.
result Extends rank-dependent utility to risk and ambiguity, reducing to existing models under specific conditions.
The paper examines expectile quadrangle properties in risk management.
problem Exploring the properties of expectile quadrangles in risk management.
method Rigorously examines the properties of expectile quadrangles.
result Rigorously examines the properties of expectile quadrangles.
The aim of this paper is to provide several examples of convex risk measures necessary for the application of the general framework for portfolio theory of Maier-Paape and Zhu, presented in Part I of this series (arXiv:1710.04579 [q-fin.PM]). As alternative to classical portfolio risk measures such as the standard devi…
Credibility theory provides tools to obtain better estimates by combining individual data with sample information. We apply the Credibility theory to a Uniform distribution that is used in testing the reliability of forecasting an interest rate for long term horizons. Such empirical exercise is asked by Regulators (CRR…
SVR analyzed within RQ framework for risk management.
problem Risk management in stochastic optimization.
method Risk Quadrangle (RQ) theory applied to SVR.
result SVR formulations as minimization of Vapnik error and CVaR norm.
Proposes a new portfolio theory that optimizes returns and risk.
problem Inefficient market hypothesis and risk premium in finance markets.
method Introduces triplet (R, H, σ) model for portfolio optimization.
result Developed a global optimal strategy for different investor styles.
The question of optimal portfolio is addressed. The conventional Markowitz portfolio optimisation is discussed and the shortcomings due to non-Gaussian security returns are outlined. A method is proposed to minimise the likelihood of extreme non-Gaussian drawdowns of the portfolio value. The theory is called Leptokurti…
This paper discusses an alternative explanation for the empirical findings contradicting the positive relationship between risk (variance) and reward (expected return). We show that these contradicting results might be due to the false definition of risk-perception, which we correct by introducing Expected Downside Ris…
The minimum description length (MDL) principle in supervised learning is studied. One of the most important theories for the MDL principle is Barron and Cover's theory (BC theory), which gives a mathematical justification of the MDL principle. The original BC theory, however, can be applied to supervised learning only …
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…
CV outperforms mean-variance for stock returns, minimizing risk and maximizing growth.
problem Traditional risk assessment methods underperform in stock market analysis.
method Derived new CV equation and used it to analyze stock performance.
result Stocks with low but positive CV grow exponentially, outperforming high-risk stocks.
A new game-theoretic approach balances downside risk with expected reward.
problem Traditional game theory views risk only from the upside perspective, ignoring downside risk.
method Introduces downside risk aware equilibria (DRAE) based on lower partial moments.
result Successfully finds equilibria that balance downside risk with expected reward.
Paper extends learning theory to dependent data with uniform risk bounds.
problem Learning with dependent data sequences.
method Derives uniform risk bounds for dependent data using VC-dimension and Rademacher complexity.
result Standard classification risk bounds hold for dependent data, same as for independent data.
New bounds for non-convex estimators without Bernstein condition.
problem Sharp excess risk bounds for non-convex and improper estimators.
method Exponential-tail local Rademacher complexity risk bounds with offset condition.
result Sharp bounds for non-convex and improper estimators without Bernstein condition.
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 …
The paper addresses human-like decision-making in multi-agent systems using bounded risk-sensitive Markov Games.
problem Modeling human-like decision-making in multi-agent systems with risk-seeking and loss-aversion behaviors.
method Forward policy design and inverse reward learning with iterative reasoning and cumulative prospect theory.
result The proposed algorithms demonstrate both risk-averse and risk-seeking behaviors in multi-agent systems.
New tool detects 'fleeting modes' causing excess risk in financial markets.
problem Detecting portfolios with statistically significant excess risk in financial markets.
method Random Matrix Theory to identify 'fleeting modes' independent of underlying correlation structure.
result Fleeting modes exist in both futures and equity markets, and momentum is a source of excess risk.
New method forecasts systemic risk with improved precision.
problem Improving the estimation of systemic risk measures.
method De-volatilizing observations and using extreme value theory for forecasting.
result Valid MES forecasts with good coverage in simulations and empirical applications.