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

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

Date10th Apr 2024

Time10:00 AM

Venue A M Turing Hall (SSB 334, Second Floor)



We consider the problems of estimation and optimization of utility-based shortfall risk (UBSR), which is a popular risk measure in finance. In the context of UBSR estimation, we derive a non-asymptotic bound on the mean-squared error of the classical sample average approximation (SAA) of UBSR. Next, in the context of UBSR optimization, we derive an expression for the UBSR gradient under a smooth parametrization. This expression is a ratio of expectations, both of which involve the UBSR. We use SAA for the numerator as well as denominator in the UBSR gradient expression to arrive at a biased gradient estimator. We derive non-asymptotic bounds on the estimation error, which show that our gradient estimator is asymptotically unbiased. We incorporate the aforementioned gradient estimator into a stochastic gradient (SG) algorithm for UBSR optimization. We then derive non-asymptotic bounds that quantify the rate of convergence of our SG algorithm for UBSR optimization.


Mr. Sumedh Sunil Gupte, Roll No: CS21D014

Computer Science and Engineering