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.
Highlights
Reverse Stress Testing (RST) is a relatively new technique for finding cases that cause a bank to cross the barrier between survival and default
We considered that other methods are not based on Bayesian Optimization (BO): binary search, random search and linear interpolation
Basel risk class Clients, Products and Business Practice was excluded because of distortions introduced by extreme losses and in accordance with BoE directives
Summary
Reverse Stress Testing (RST) is a relatively new technique for finding cases that cause a bank to cross the barrier between survival and default. Bank default can lead to a chain of further defaults, so determining how RST should be done is vital for limiting systemic risk. In which outcomes resulting from amended model parameters are calculated, is more common and is a regulatory requirement. We suggest an optimal way to do RST in the context of operational risk, which is the risk of incurring financial loss from adverse events. We make a significant improvement to an established optimization method and provide evidence that our suggestion is, optimal. Sufficient guidance for practitioners is given to enable sufficiently accuracy to be achieved
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