Rearrangement Algorithm in Risk Aggregation

Sometimes there’s no closed-form analytical solutions for the risk measure of aggregate losses representing, say, a company’s losses in each country or city it operates in, a portfolio of losses subdivided by investment, or claims made by clients to an insurance company. Assuming there’s enough data to assign a distribution to those losses, we examine the Rearrangement Algorithm’s ability to numerically compute the Expected Shortfall and Exponential Premium Principle/Entropic Risk Measure of aggregate losses. A more efficient discretization scheme is introduced and the algorithm is extended to the Entropic Risk Measure which turns out to have a smaller uncertainty spread than the Expected Shortfall at least for the cases that we examined.