Online Estimation and Optimization of Utility-Based Shortfall Risk

• 成果类型: Article; Early Access
• 署名作者: Hegde, Vishwajit; Menon, Arvind Satish; Prashanth, L. A.; Tagannathan, Krishna
• 署名单位: Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Madras; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Madras; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Madras
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0266
• 发表日期: 2024
• 关键词: stochastic-approximation; hilbert-spaces; INFORMATION; efficient; bounds; rates

摘要

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, in which 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 estimation schemes. We derive nonasymptotic 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 nonasymptotic bounds on its convergence.