Tail Conditional Expectations for Extended Exponential Dispersion Models

Abstract

For a loss that can be incurred in a given period, the tail conditional expectation, also termed as tail value-at-risk, is the conditional average amount of loss, given that the loss exceeds a specified value. This measurement helps insurance companies to determine the amounts of capital to pay out claims resulted from catastrophic event when premium revenues are insufficient. In this paper, we extend the exponential dispersion models and derive tail conditional expectation forms of the extended models.