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Cox risk model with correlated classes of business. (English) Zbl 1212.91042

Summary: 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, an explicit expression of the Lundberg exponent is derived under a special condition.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
60G46 Martingales and classical analysis
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References:

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