Shortfall Deviation Risk: An alternative to risk measurement

We present the Shortfall Deviation Risk (SDR), a risk measure that represents the expected loss that occur with certain probability penalized by the dispersion of results worse than such expectation. SDR combines Expected Shortfall (ES) and Shortfall Deviation (SD), which we also introduce, contemplating two fundamental pillars of the risk concept, the probability of adverse events (ES) and the variability of an expectation (SD), and considers extreme results. We demonstrate that SD is a generalized deviation measure, whereas SDR is a coherent risk measure. We achieve the dual representation of SDR, and we discuss issues such as its representation by a weighted ES, acceptance sets, convexity, continuity and relationship with stochastic dominance.