Utility‐based shortfall risk: Efficient computations via Monte Carlo

Abstract

With the development of financial risk management, the notion of convex risk measures has been proposed and has gained increasing attentions. Utility‐based shortfall risk (SR), as a specific and important class of convex risk measures, has become popular in recent years. In this paper we focus on the computational aspects of SR, which are significantly understudied but fundamental for risk assessment and management. We discuss efficient estimation, optimization, and sensitivity analysis of SR, based on Monte Carlo techniques and stochastic optimization methods. We also conduct extensive numerical studies on the proposed approaches. The numerical results further demonstrate the effectiveness of these approaches.

A Survey of Risk-Aware Multi-Armed Bandits

“…Further, if the utility is increasing, then the estimation of UBSR from i.i.d. samples can be performed in a computationally efficient manner; see Hu and Zhang (2018).…”

“…. , X n , we use the following sample-average approximation to the optimization problem in (3) (also see Hu and Zhang (2018)):…”

“…As in the case of CVaR and SRM, the UBSR estimator provided above is a special case of the general estimate given by ρ n := ρ(F n ). Further, the estimation problem in (4) can be solved in a computationally efficient fashion using a bisection method; see Hu and Zhang (2018).…”

“…For example, if we have an important face-to-face meeting downtown, we might want to choose a route that has a slightly higher expected travel time, but whose variance is small. Some risk measures include the mean-variance (Markowitz, 1952), the conditional value-atrisk (Artzner et al, 1999;Rockafellar and Uryasev, 2000), spectral risk measures (Acerbi, 2002), utility-based shortfall risk (Artzner et al, 1999;Hu and Zhang, 2018), and cumulative prospect theory (Tversky and Kahneman, 1992). This short survey aims to consolidate these various risk measures and to comment on their concentration properties.…”