Maxentropic Approach to Decompound Aggregate Risk Losses

A risk manager may be faced with the following problem: she/he has obtained loss data collected during a year, but the data only contains the total number events and the total loss for that year. She/he suspects that there are different sources of risk, each occurring with a different frequency, and wants to identify the frequency with which each type of event occurs and if possible, the individual losses at each risk event.It is the purpose of this methodological note, to examine a combination of disentangling and decompounding procedures to get as close as possible to that goal. The disentangling procedure is used to determine the frequencies of each type of risk and the decompounding to determine the distribution of individual losses that aggregated yield the observed total loss