Feasible fraud and auditing probabilities for insurance companies and policyholders

Insurance claims fraud is counted among the major concerns in the insurance industry, the reason being that excess payments due to fraudulent claims account for a large percentage of the total payments each year. We formulate optimization problems from the insurance company as well as the policyholder perspective based on a costly state verification approach. In this setting—while the policyholder observes his losses privately—the insurance company can decide to verify the truthfulness of incoming claims at some cost. We show simulation results illustrating the agreement range which is characterized by all valid fraud and auditing probability combinations both stakeholders are willing to accept. Furthermore, we present the impact of different valid probability combinations on the insurance company's and the policyholder's objective quantities and analyze the sensitivity of the agreement range with respect to a relevant input parameter. This contribution summarizes the major findings of a working paper written by Müller etal. (Working Papers on Risk Management and Insurance (IVW-HSG), No. 92, 2011