Online Estimation and Optimization of Utility-Based Shortfall Risk
This work addresses risk management in finance by providing efficient online algorithms for UBSR, but it is incremental as it builds on existing stochastic methods for a specific risk metric.
The paper tackles the problem of estimating and optimizing Utility-Based Shortfall Risk (UBSR) in a recursive, online setting using stochastic approximation and gradient descent methods, deriving non-asymptotic error bounds for estimation and convergence bounds for optimization.
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.