Extreme Risk Measures: Estimation and Optimization via Stochastic Approximation
Abstract: Risk measures such as Value at Risk (VaR) and Conditional Value at Risk (CVaR) are critical to evaluating performance in high-risk scenarios such as high-frequency trading, healthcare, risk-sensitive control and insurance. VaR quantifies the maximum potential return over a specified time horizon at a given confidence level, while CVaR extends this by estimating the expected return exceeding the VaR threshold. Estimating the extreme version of these risk measures is inherently sensitive and volatile due to the limited data available at the tail end of the return distribution. This paper introduces an incremental, single-pass, and adaptive variance reduction techniques to estimate extreme VaR and CVaR for cases where the underlying distribution is either known or unknown. Additionally, we present a multi-time scale method to optimize CVaR within a parameterized distribution space in an online fashion. We provide both theoretical and empirical analyses to demonstrate the effectiveness and competitiveness of our proposed approaches.
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Matthew_J._Holland1
Submission Number: 3266
Loading