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Shortfall as a risk measure: properties, optimization and applications. (English) Zbl 1200.91133
Summary: Motivated from second-order stochastic dominance, we introduce a risk measure that we call shortfall. We examine shortfall’s properties and discuss its relation to such commonly used risk measures as standard deviation, VaR, lower partial moments, and coherent risk measures. We show that the mean-shortfall optimization problem, unlike mean-VaR, can be solved efficiently as a convex optimization problem, while the sample mean-shortfall portfolio optimization problem can be solved very efficiently as a linear optimization problem. We provide empirical evidence (a) in asset allocation, and (b) in a problem of tracking an index using only a limited number of assets that the mean-shortfall approach might have advantages over mean-variance.

MSC:
91B30 Risk theory, insurance (MSC2010)
60E15 Inequalities; stochastic orderings
90C15 Stochastic programming
91G10 Portfolio theory
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