Backtesting general spectral risk measures with application to expected shortfall

2015 ◽  
Vol 9 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Nick Costanzino ◽  
Mike Curran
Keyword(s):  
Risk Measures ◽  
Expected Shortfall ◽  
Spectral Risk Measures

Distributional Uncertainty for Spectral Risk Measures

2021 ◽  
pp. 476-494
Author(s):  
Mohammed Berkhouch
Keyword(s):  
Risk Assessment ◽  
Financial Market ◽  
Financial Crises ◽  
Risk Measures ◽  
Expected Shortfall ◽  
Risk Measurement ◽  
Spectral Risk Measures ◽  
Quantifying Uncertainty ◽  
Financial Losses ◽  
Robust Framework

Spectral risk measures, primarily introduced as an extension for expected shortfall, constitute a prominent class of risk measures that take account of the decision-makersrisk-aversion. In practice, risk measures are often estimated from data distributions, and due to the uncertain character of the financial market, one has no specific criterium to pick the appropriate distribution. Therefore, risk assessment under different possible scenarios (such as financial crises or outbreaks) is a source of uncertainty that may lead to concerning financial losses. The chapter addresses this issue, first, by adapting a robust framework for spectral risk measures, by considering the whole set of possible scenarios instead of making a specific choice. Second, the author proposes a variability-type approach as an alternative for quantifying uncertainty, since measuring uncertainty provides us with information about how far our risk measurement process could be impacted by uncertainty. Furthermore, the stated theory is illustrated with a practical example from the NASDAQ index.

scholarly journals Minimizing spectral risk measures applied to Markov decision processes

2021 ◽  
Author(s):  
Nicole Bäuerle ◽  
Alexander Glauner
Keyword(s):  
Minimization Problem ◽  
Risk Measures ◽  
Risk Measure ◽  
Sufficient Conditions ◽  
Planning Horizon ◽  
Insurance Company ◽  
Existence Of A Solution ◽  
Discounted Cost ◽  
Spectral Risk Measures ◽  
Markov Decision

AbstractWe study the minimization of a spectral risk measure of the total discounted cost generated by a Markov Decision Process (MDP) over a finite or infinite planning horizon. The MDP is assumed to have Borel state and action spaces and the cost function may be unbounded above. The optimization problem is split into two minimization problems using an infimum representation for spectral risk measures. We show that the inner minimization problem can be solved as an ordinary MDP on an extended state space and give sufficient conditions under which an optimal policy exists. Regarding the infinite dimensional outer minimization problem, we prove the existence of a solution and derive an algorithm for its numerical approximation. Our results include the findings in Bäuerle and Ott (Math Methods Oper Res 74(3):361–379, 2011) in the special case that the risk measure is Expected Shortfall. As an application, we present a dynamic extension of the classical static optimal reinsurance problem, where an insurance company minimizes its cost of capital.

scholarly journals On the existence of an optimal estimation window for risk measures

2015 ◽  
Vol 4 (1and2) ◽  
pp. 28
Author(s):  
Marcelo Brutti Righi ◽  
Paulo Sergio Ceretta
Keyword(s):  
At Risk ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Value At Risk ◽  
Financial Risk ◽  
Risk Measures ◽  
Optimal Estimation ◽  
Expected Shortfall ◽  
Estimation Bias ◽  
Optimal Length

We investigate whether there can exist an optimal estimation window for financial risk measures. Accordingly, we propose a procedure that achieves optimal estimation window by minimizing estimation bias. Using results from a Monte Carlo simulation for Value at Risk and Expected Shortfall in distinct scenarios, we conclude that the optimal length for the estimation window is not random but has very clear patterns. Our findings can contribute to the literature, as studies have typically neglected the estimation window choice or relied on arbitrary choices.

A new class of spectral risk measures

2018 ◽  
Author(s):  
Mohammed Berkhouch ◽  
Ghizlane Lakhnati ◽  
Marcelo Brutti Righi
Keyword(s):  
Risk Measures ◽  
New Class ◽  
Spectral Risk Measures

INSTABILITY OF PORTFOLIO OPTIMIZATION UNDER COHERENT RISK MEASURES

2010 ◽  
Vol 13 (03) ◽  
pp. 425-437 ◽  
Author(s):  
IMRE KONDOR ◽  
ISTVÁN VARGA-HASZONITS
Keyword(s):  
Portfolio Optimization ◽  
Risk Measures ◽  
Risk Measure ◽  
Expected Shortfall ◽  
Optimal Portfolio ◽  
The Other ◽  
Coherent Risk Measures ◽  
Coherent Risk ◽  
Large Samples

It is shown that the axioms for coherent risk measures imply that whenever there is a pair of portfolios such that one of them dominates the other in a given sample (which happens with finite probability even for large samples), then there is no optimal portfolio under any coherent measure on that sample, and the risk measure diverges to minus infinity. This instability was first discovered in the special example of Expected Shortfall which is used here both as an illustration and as a springboard for generalization.

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