The compound Poisson risk model with multiple thresholds
presented by Kristina P. Sendova
There exist a wide variety of models attempting to describe the surplus process of an insurance company. Motivated by the notion that an insurer should be able to change premium rates depending on the company's current surplus, we consider a multi-threshold compound Poisson risk model. We further solve a general integro-differential equation with potential applications to ruin theory problems. Consequently, an important particular case is discussed. Namely, the so called Gerber-Shiu discounted penalty function under the compound Poisson model with multiple thresholds. Finally, examples are considered to illustrate the applicability of the main result.