Online Estimation and Optimization of Utility-Based Shortfall Risk

Vishwajit Hegde, Arvind S. Menon, L. A. Prashanth and Krishna Jagannathan

Papers from arXiv.org

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.

Date: 2021-11, Revised 2023-11
New Economics Papers: this item is included in nep-ecm, nep-rmg and nep-upt
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