On a risk model with random incomes and dependence between claim sizes and claim intervals |
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Authors: | Jie-hua Xie Wei Zou |
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Affiliation: | Department of Science, NanChang Institute of Technology, NanChang 330099, PR China |
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Abstract: | In this paper, we construct a risk model with a dependence setting where there exists a specific structure among the time between two claim occurrences, premium sizes and claim sizes. Given that the premium size is exponentially distributed, both the Laplace transforms and defective renewal equations for the expected discounted penalty functions are obtained. Exact representations for the solutions of the defective renewal equations are derived through an associated compound geometric distribution. When the claims are subexponentially distributed, the asymptotic formulae for ruin probabilities are obtained. Finally, when the individual premium sizes have rational Laplace transforms, the Laplace transforms for the expected discounted penalty functions are obtained. |
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Keywords: | Compound Poisson risk model Expected discounted penalty function Random income Defective renewal equation Heavy-tailed distribution |
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