Conditional g-expectation is applied to define (dynamic) risk measures, which satisfies the axioms of coherent (dynamic) risk measures. Then, the representation theorems of the given (dynamic) coherent risk measures are provided.
In the second part, we introduce Markowitz Investment Theory, E-V Model, E-SV Model and some other important risks measurement. These theories are important parts in modern risks management theories. They are also basis of VaR and CVaR.
After discussing the state of the art of operational risk measurement, I briefly review the foundations of input-output analysis and explain how to build an input-output model at the business unit level for a financial institution.
The model is then enlarged to allow its use for interest rate risk measurement through a duration vector.
In this paper they are applied to risk measurement, leading to a general definition of convex risk measure which corresponds, when its domain is a linear space, to the one recently introduced in risk measurement literature.
Study on the interrelation of efficient portfolios and their frontier under t distribution and various risk measures
Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared.
When the insurer and reinsurance company take arbitrary risk measures, sufficient conditions for optimality of reinsurance contract are given within the restricted class of admissible contracts.
Further, the explicit forms of optimal reinsurance contract under several special risk measures are given, and the method to decide parameters as well.
For these systems, effective algorithms for computing probability indexes (risk levels) and loss expectation (risk measures) for undesirable random events (failures, emergencies, etc.) associated with the operation of a system are designed.