Omega Model for a Jump-Diffusion Process

A jump-diffusion Omega model is studied in this paper. In this model, the surplus process is a perturbation of a compound Poisson process by a Brown motion. For exponential claim size and constant bankruptcy rate function, several explicit formulae on bankruptcy probability for the model are derived. The relationship between bankruptcy probability and occupation time in the red is also discussed. Then numerical examples are given to show some comparisons for the model with the Omega model of Albrecher and Lautscham (2013).