Numerical Method for the Perturbed Risk Model with Randomized Observation and Two-sided Jumps
Hua Dong *
School of Statistics, Qufu Normal University, Shandong 273165, China.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we considered the perturbed risk model with two-sided jumps, where ruin can only occur at some Poisson times. A generalized Gerber-Shiu-type function is discussed involving the number of observations, the ruin time and the de cit at ruin. Integro-differential equations with certain boundary conditions are derived. As it is diffcult to get closed-form solutions, a numerical sinc method is proposed.
Keywords: Randomized observation times, two-sided jumps, gerber-Shiu-type function