Operational Risk Reverse Stress Testing: Optimal Solutions

Abstract

Selecting a suitable method to solve a black-box optimization problem that uses noisy data was considered. A targeted stop condition for the function to be optimized, implemented as a stochastic algorithm, makes established Bayesian methods inadmissible. A simple modification was proposed and shown to improve optimization the efficiency considerably. The optimization effectiveness was measured in terms of the mean and standard deviation of the number of function evaluations required to achieve the target. Comparisons with alternative methods showed that the modified Bayesian method and binary search were both performant, but in different ways. In a sequence of identical runs, the former had a lower expected value for the number of runs needed to find an optimal value. The latter had a lower standard deviation for the same sequence of runs. Additionally, we suggested a way to find an approximate solution to the same problem using symbolic computation. Faster results could be obtained at the expense of some impaired accuracy and increased memory requirements.