Abstract
This paper considers a perturbed Markov‐modulated risk model with two‐sided jumps, where both the upward and downward jumps follow arbitrary distribution. We first derive a system of differential equations for the Gerber‐Shiu function. Furthermore, a numerical result is given based on Chebyshev polynomial approximation. Finally, an example is provided to illustrate the method.
Highlights
The risk model with two-sided jumps was first proposed by Boucherie et al 1 and has been further investigated by many authors during the last few years
The upward jumps can be explained as the random income premium or investment, while the downward jumps are interpreted as the random loss
For δ ≥ 0, let φi u E e−δT ω U T −, |U T | I T < ∞ | J 0 i, U 0 u, u ≥ 0, 1.4 be the Gerber-Shiu function at ruin given that the initial state is i, where ω x1, x2 is a nonnegative penalty function, U T − is the surplus immediately prior to ruin, and |U T | is the deficit at ruin
Summary
This paper considers a perturbed Markov-modulated risk model with two-sided jumps, where both the upward and downward jumps follow arbitrary distribution. We first derive a system of differential equations for the Gerber-Shiu function. A numerical result is given based on Chebyshev polynomial approximation. An example is provided to illustrate the method
Sign-in/Register to view highlights & summary 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 callDisclaimer: 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.
