A Framework for Measures of Risk under Uncertainty

@article{Fadina2021AFF,
  title={A Framework for Measures of Risk under Uncertainty},
  author={Tolulope Fadina and Yang Liu and Ruodu Wang},
  journal={SSRN Electronic Journal},
  year={2021}
}
A risk analyst assesses potential financial losses based on multiple sources of information. Often, the assessment does not only depend on the specification of the loss random variable, but also various economic scenarios. Motivated by this observation, we design a unified axiomatic framework for risk evaluation principles which quantifies jointly a loss random variable and a set of plausible probabilities. We call such an evaluation principle a generalized risk measure. We present a series of… 

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References

SHOWING 1-10 OF 42 REFERENCES
Risk Preferences and Their Robust Representation
TLDR
This work describes the subjective notion of risk by means of a risk order and focuses on the context invariant features of diversification and monotonicity, which allows for a differentiated interpretation depending on the underlying context that is illustrated in different settings.
Quantile-Based Risk Sharing
TLDR
It is shown that, in general, a robust optimal allocation exists if and only if none of the underlying risk measures is a VaR, and several novel advantages of ES over VaR from the perspective of a regulator are revealed.
An Axiomatic Foundation for the Expected Shortfall
In the recent Basel Accords, the Expected Shortfall (ES) replaces the Value-at-Risk (VaR) as the standard risk measure for market risk in the banking sector, making it the most popular risk measure
Scenario-Based Risk Evaluation
Risk measures such as Expected Shortfall (ES) and Value-at-Risk (VaR) have been prominent in banking regulation and financial risk management. Motivated by practical considerations in the assessment
Coherent Measures of Risk
In this paper we study both market risks and nonmarket risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable
Maxmin Expected Utility with Non-Unique Prior
Attitude toward imprecise information
Robustness in the Optimization of Risk Measures
TLDR
It is discovered that for many simple representative optimization problems, VaR generally leads to non-robust optimizers whereas ES generally leadsto robust ones.
Prospect Theory: For Risk and Ambiguity
Preface Introduction Part I. Expected Utility: 1. The general model of decision under uncertainty no-arbitrage (expected utility with known utilities and unknown probabilities) 2. Expected utility
Stochastic Finance: An Introduction in Discrete Time
This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in
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4
5
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