Modeling of risk losses using size-biased data

In this paper we present a method for drawing inferences about the process of financial losses that are associated with the operations of a business. For example, for a bank such losses may be related to erroneous transactions, human error, fraud, lawsuits, or power outages. Information about the frequency and magnitude of losses is obtained through the search of a number of sources, such as printed, computerized, or Internet-based publications related to insurance and finance. The data consists of losses that were discovered in the search. We assume that the probability of a loss appearing in the body of sources and also being discovered increases with the magnitude of the loss. Our approach simultaneously models the process of losses and the process of populating the database. The approach is illustrated using data related to operational risk losses that are of special interest to the banking industry.