Efficient Importance Sampling for Utility-Based Shortfall Risk

The objective of this paper is to study the effect of efficient importance sampling (EIS) techniques on simulating the distribution-invariant convex risk measures: utility-based shortfall risk measures (USR). We firstly introduce EIS to simulate USR based on nonlinear Generalized Least Squares and demonstrate how to choose a candidate density in the context of multi-normal distributions. After presenting the construction of our algorithm, we apply our efficient scheme for calculating Entropic risk measure under the setting of the mixed Poisson model of CreditRisk⁺. We furthermore make an improvement for EIS so that we can calculate USR with piecewise polynomial function loss functions. Finally, the method is applied to an example to demonstrate its performance and flexibility.