We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimat...We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimate ruin probability when the inter-claim times are exponentially distributed. A defective renewal equation satisfied by the ultimate ruin probability is then given. For the general inter-claim times with zero-truncated geometrically distributed claim sizes, the explicit expression for the ultimate ruin probability is derived.展开更多
基金National Basic Research Program of China(973 Program No.2007CB814903)the National Natural Science Foundation of China(No.70671069)
文摘We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimate ruin probability when the inter-claim times are exponentially distributed. A defective renewal equation satisfied by the ultimate ruin probability is then given. For the general inter-claim times with zero-truncated geometrically distributed claim sizes, the explicit expression for the ultimate ruin probability is derived.
