Abstract

PurposeThe purpose of this article is to consider the classical risk model that is perturbed by a Brownian motion process. The article derives explicit formulas for the joint and marginal probability density functions of the surplus prior to ruin and the deficit at ruin.Design/methodology/approachThis article first extends the dual argument to probabilistically explain the symmetry between the two random variables related to the so‐called modified ladder height. Then the paper uses renewal arguments to derive the joint distribution of the surplus prior to ruin and the deficit at ruin.FindingsThe study derived an explicit formula for the undiscounted joint density in the perturbed risk model that is directly parallel to formula (3.2) for the classical risk model. The formula clearly shows that in a perturbed risk process, when ruin is caused by a claim, the p.d.f. of the surplus prior to ruin is continuous. In addition, shows that when the claim sizes follow a phase‐type distribution, all the relevant quantities can be conveniently computed.Originality/valueThe dual argument used in this article is novel. The formula first clearly shows that in the perturbed risk model, the p.d.f. of the surplus prior to ruin is continuous. When claim sizes are phase‐type, the formulas can be conveniently computed.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.