2021/11/16 by Hegde, Vishwajit, Arvind S. Menon, Menon, Arvind S. +3 · 3 citations
Decision Sciences · Mathematics · #FOS: Computer and information sciences #FOS: Economics and business #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Probability and Risk Models #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2111.08805
openalex publication_date 2021/11/16 · openalex created_date 2022/10/24 · openalex updated_date 2026/07/28
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.