On the cost of risk misspecification in insurance pricing

In the non-life insurance industry, pricing is often done relative to individual criteria of policyholders. Various classification algorithms are in use to categorize policyholders into risk classes defined by the insurer, but classification errors may result from this process. In the light of recent automatic classification practices, it becomes important to assess the risks caused by such errors. In this paper we examine the impact of risk class misspecifications for a simple situation with two risk types. We provide a mean-variance framework for quantitatively studying the insurer's optimization problem of specifying premiums and we analyze the tradeoff of costs and benefits when classification error probabilities are known.