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We consider the problems of estimation and optimization of utility-basedshortfall risk (UBSR), which is a popular risk measure in finance. In thecontext of UBSR estimation, we derive a non-asymptotic bound on themean-squared error of the classical sample average approximation (SAA) of UBSR.Next, in the context of UBSR optimization, we derive an expression for the UBSRgradient under a smooth parameterization. This expression is a ratio ofexpectations, both of which involve the UBSR. We use SAA for the numerator aswell as denominator in the UBSR gradient expression to arrive at a biasedgradient estimator. We derive non-asymptotic bounds on the estimation error,which show that our gradient estimator is asymptotically unbiased. Weincorporate the aforementioned gradient estimator into a stochastic gradient(SG) algorithm for UBSR optimization. Finally, we derive non-asymptotic boundsthat quantify the rate of convergence of our SG algorithm for UBSRoptimization.

Optimization of utility-based shortfall risk: A non-asymptotic viewpoint