Estimating Reinsurance Premiums Using Extreme Value Theory with Claim Payment Delay Adjustment

Abstract

Extreme losses play an important role in reinsurance pricing, particularly for excess-of-loss contracts where classical parametric models often fail to adequately capture tail risk. Extreme Value Theory (EVT) provides a theoretically justified framework for modeling heavy-tailed insurance losses; however, most existing studies focus mainly on claim severity and ignore operational characteristics such as claim payment delay. This study proposes an EVT-based reinsurance premium estimation framework that incorporates claim payment delay as a risk modifier. Using a peaks over threshold approach, exceedances above a high threshold are modeled by the Generalized Pareto Distribution, and tail-based reinsurance premiums are derived under the net premium principle. An empirical application using claim data shows that claim severity exhibits heavy-tailed behavior and that EVT provides an adequate fit to extreme losses. Furthermore, incorporating payment delay leads to systematically higher estimated reinsurance premiums, indicating the importance of considering settlement dynamics in pricing. The proposed framework provides a practical extension of EVT-based reinsurance premium estimation by integrating tail risk and operational risk in a unified approach.