Risk level upper bounds with general risk functions

In the last teen years many new risk functions have been introduced (coherent risk measures, expectation bounded risk measures, generalized deviations, etc.) and many actuarial and/or financial problems have been revisited by using them. The use of new risk functions is well justified by the rapid development and evolution of the financial markets and the growing presence of skewness and kurtosis, among many other reasons, but the practical final result of many problems may critically depend on the concrete risk function we are drawing on. This paper deals with optimization problems involving risk functions and proposes several risk level upper bounds that apply regardless of the considered function. In particular both capital requirements and usual central moments and dispersions are bounded from above. The methodology is general enough and applies for perfect or imperfect financial markets, static or dynamic models, pricing or hedging issues, portfolio choice problems, optimal reinsurance problems, etc.

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