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
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