Optimal Catastrophe Reinsurance Contract Design Using Tail Risk Measures

2015 ◽  
Author(s):  
Frank Yulin Feng
Keyword(s):  
Risk Measures ◽  
Contract Design ◽  
Tail Risk ◽  
Catastrophe Reinsurance

A Theory for Measures of Tail Risk

2021 ◽  
Author(s):  
Fangda Liu ◽  
Ruodu Wang
Keyword(s):  
Value At Risk ◽  
Financial Regulation ◽  
Risk Measures ◽  
Risk Measure ◽  
Continuity Condition ◽  
Tail Risk ◽  
Dual Representations ◽  
Joint Properties ◽  
Risk Aggregation ◽  
Popular Classes

The notion of “tail risk” has been a crucial consideration in modern risk management and financial regulation, as very well documented in the recent regulatory documents. To achieve a comprehensive understanding of the tail risk, we carry out an axiomatic study for risk measures that quantify the tail risk, that is, the behaviour of a risk beyond a certain quantile. Such risk measures are referred to as tail risk measures in this paper. The two popular classes of regulatory risk measures in banking and insurance, value at risk (VaR) and expected shortfall, are prominent, yet elementary, examples of tail risk measures. We establish a connection between a tail risk measure and a corresponding law-invariant risk measure, called its generator, and investigate their joint properties. A tail risk measure inherits many properties from its generator, but not subadditivity or convexity; nevertheless, a tail risk measure is coherent if and only if its generator is coherent. We explore further relevant issues on tail risk measures, such as bounds, distortion risk measures, risk aggregation, elicitability, and dual representations. In particular, there is no elicitable tail convex risk measure other than the essential supremum, and under a continuity condition, the only elicitable and positively homogeneous monetary tail risk measures are the VaRs.

Optimal Reinsurance Arrangements Under Tail Risk Measures

2009 ◽  
Vol 76 (3) ◽  
pp. 709-725 ◽  
Author(s):  
Carole Bernard ◽  
Weidong Tian
Keyword(s):  
Risk Measures ◽  
Tail Risk ◽  
Optimal Reinsurance

scholarly journals Problem-driven scenario generation: an analytical approach for stochastic programs with tail risk measure

2019 ◽  
Author(s):  
Jamie Fairbrother ◽  
Amanda Turner ◽  
Stein W. Wallace
Keyword(s):  
Portfolio Selection ◽  
Random Vector ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Monte Carlo Sampling ◽  
Conditional Value At Risk ◽  
Scenario Generation ◽  
Tail Risk ◽  
Stochastic Programs

AbstractScenario generation is the construction of a discrete random vector to represent parameters of uncertain values in a stochastic program. Most approaches to scenario generation are distribution-driven, that is, they attempt to construct a random vector which captures well in a probabilistic sense the uncertainty. On the other hand, a problem-driven approach may be able to exploit the structure of a problem to provide a more concise representation of the uncertainty. In this paper we propose an analytic approach to problem-driven scenario generation. This approach applies to stochastic programs where a tail risk measure, such as conditional value-at-risk, is applied to a loss function. Since tail risk measures only depend on the upper tail of a distribution, standard methods of scenario generation, which typically spread their scenarios evenly across the support of the random vector, struggle to adequately represent tail risk. Our scenario generation approach works by targeting the construction of scenarios in areas of the distribution corresponding to the tails of the loss distributions. We provide conditions under which our approach is consistent with sampling, and as proof-of-concept demonstrate how our approach could be applied to two classes of problem, namely network design and portfolio selection. Numerical tests on the portfolio selection problem demonstrate that our approach yields better and more stable solutions compared to standard Monte Carlo sampling.

Efficient Nested Simulation Of Tail Risk Measures

2019 ◽  
Author(s):  
Jessica O. Dang ◽  
Ben M. Feng ◽  
Mary R. Hardy
Keyword(s):  
Risk Measures ◽  
Tail Risk

Beyond reasonable doubt: multiple tail risk measures applied to European industries

2012 ◽  
Vol 19 (7) ◽  
pp. 671-676 ◽  
Author(s):  
David Edmund Allen ◽  
Robert John Powell ◽  
Abhay Kumar Singh
Keyword(s):  
Risk Measures ◽  
Reasonable Doubt ◽  
Tail Risk

ESTIMATION OF HIGH CONDITIONAL TAIL RISK BASED ON EXPECTILE REGRESSION

2021 ◽  
pp. 1-32
Author(s):  
Jie Hu ◽  
Yu Chen ◽  
Keqi Tan
Keyword(s):  
Quantile Regression ◽  
Value At Risk ◽  
Risk Measures ◽  
Asymptotic Properties ◽  
Estimation Method ◽  
Real Data ◽  
Tail Index ◽  
Tail Risk ◽  
Expectile Regression ◽  
Quantile Regression Method

Abstract Assessing conditional tail risk at very high or low levels is of great interest in numerous applications. Due to data sparsity in high tails, the widely used quantile regression method can suffer from high variability at the tails, especially for heavy-tailed distributions. As an alternative to quantile regression, expectile regression, which relies on the minimization of the asymmetric l2-norm and is more sensitive to the magnitudes of extreme losses than quantile regression, is considered. In this article, we develop a new estimation method for high conditional tail risk by first estimating the intermediate conditional expectiles in regression framework, and then estimating the underlying tail index via weighted combinations of the top order conditional expectiles. The resulting conditional tail index estimators are then used as the basis for extrapolating these intermediate conditional expectiles to high tails based on reasonable assumptions on tail behaviors. Finally, we use these high conditional tail expectiles to estimate alternative risk measures such as the Value at Risk (VaR) and Expected Shortfall (ES), both in high tails. The asymptotic properties of the proposed estimators are investigated. Simulation studies and real data analysis show that the proposed method outperforms alternative approaches.

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