Online Estimation and Optimization of Utility-Based Shortfall Risk

• URL: http://arxiv.org/abs/2111.08805v3
• Date: Mon, 27 Nov 2023 18:24:41 GMT
• Title: Online Estimation and Optimization of Utility-Based Shortfall Risk
• Authors: Vishwajit Hegde, Arvind S. Menon, L.A. Prashanth, and Krishna Jagannathan
• Abstract summary: We consider the problem of estimating Utility-Based Shortfall Risk (UBSR) We cast the UBSR estimation problem as a root finding problem, and propose approximation-based estimations schemes. We derive non-asymptotic bounds on the estimation error in the number of samples.
• Score: 0.9999629695552195
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Utility-Based Shortfall Risk (UBSR) is a risk metric that is increasingly popular in financial applications, owing to certain desirable properties that it enjoys. We consider the problem of estimating UBSR in a recursive setting, where samples from the underlying loss distribution are available one-at-a-time. We cast the UBSR estimation problem as a root finding problem, and propose stochastic approximation-based estimations schemes. We derive non-asymptotic bounds on the estimation error in the number of samples. We also consider the problem of UBSR optimization within a parameterized class of random variables. We propose a stochastic gradient descent based algorithm for UBSR optimization, and derive non-asymptotic bounds on its convergence.

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