We consider the Sparre Andersen model modified by the inclusion of interest on the surplus. Approximation for the ultimate ruin probability is derived by rounding. And upper bound and lower bound are also derived by rounding-down and rounding-up respectively. According to the upper bound and lower bound, we can easily obtain the error estimation of the approximation. Applications of the results to the compound Poisson model are given.
A measure-valued diffusion process describing how the measures evolve under flows or "imaginary" flows on Rd is constructed in this paper. The interest of the process is that on the one hand, it can be viewed as a measure-valued flow; on the other hand, the general stochastic flows of measurable maps or kernels do not cover it.
