scholarly journals The theory and application of spectral risk measures in Vietnam

2017 ◽  
Vol 24 (4) ◽  
pp. 29-45
Author(s):  
Ho Hong Hai ◽  
Nguyen Thi Hoa
Keyword(s):  
Risk Measures ◽  
Spectral Risk Measures

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.

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

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.

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