|
Information and Service
|
|
| This Article | |
 |
Supporting info |
|
PDF(258KB) |
|
[HTML] |
|
Reference |
| Service and feedback | |
|
Add to Citation Manager |
|
Cite This Article |
|
Email Alert |
| Keywords | |
|
Sparre Andersen risk model |
|
Erlang($n$) |
|
Gerber-Shiu function |
|
ruin probability. |
| Authors | |
|
Fan Qingzhu:Yin Chuancun |
| PubMed | |
|
Article by |
The Gerber-Shiu Function for a Sparre Andersen\\Risk Model
Fan Qingzhu:Yin Chuancun
Department of Statistics and Finance, School of Business, Shihezi University School of Mathematical Sciences, Qufu Normal University
In this paper, we consider a Sparre Andersen risk model in which
the claim inter-arrival distribution is a mixture of an Erlang($n$)
distribution and an Erlang($m$) distribution. Our purpose is to
study the Gerber-Shiu function $\phi_\delta(u)$. First, we show that
$\phi_\delta(u)$ satisfies a higher-order integro-differential
equation, and then we discuss the roots of the generalized
Lundberg's equation. On this basis, we drive the Laplace transform
of $\phi_\delta(u)$ and prove that $\phi_\delta(u)$ satisfies a
renewal equation. Finally, we consider an example.