Cox Risk Model with Correlated Classes of Business

摘要

A correlated aggregate claim model with m dependent classes of insurance business is constructed, in which claim occurrences of m classes relate to Cox process and these claim processes are correlated. This Cox risk model with correlated classes of business is first transformed to the Cox model of n independent risk processes. Then the generalized Lundberg exponent and Lundberg inequality are obtained by the martingale approach. Finally, the explicit expression of Lundberg exponent under a special condition is derived.