Operations which form new risk measures from a collection of given (often simpler) risk measures have been used extensively in the literature. Examples include convex combination, convolution, and the worst-case operator. Here we study the risk measure that is constructed from a family of given risk measures by the best-case operator; that is, the newly constructed risk measure is defined as th...

In this talk, we focus on a convex risk measure which is induced by the shortfall risk, which is defined as the weighted expectation by some loss function of the positive part of the difference between a claim and a portfolio value at the maturity of our market. The convex risk measure concerned in this talk expresses the least cost to suppress its shortfall risk below the threshold being deter...

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This paper introduces an axiom of excess invariance for risk measures, meaning insensitivity to the amount by which a portfolio’s value exceeds a benchmark. The paper also introduces the class of shortfall risk measures, which are excess-invariant as well as normalized, non-negative, and monotone non-increasing. Shortfall risk measures are suitable for regulatory or risk management applications...