Gerber-Shiu Function in the Compound Poisson Risk Model perturbed by diffusion under a Barrier Strategy

DOI

10.2991/meic-14.2014.51How to use a DOI?

Keywords

Barrier strategy; Diffusion process; Compound poisson process; Gerber-Shiu function; Integro-differential

Abstract

People who work in the field of actuarial science pay more and more attention to the risk model with dividend strategy, it has become one of the hot topics in the current actuarial science research. In this paper, we want to study the Gerber-Shiu expected discounted penalty function due to oscillation which written as , considering a classical compound poisson risk model perturbed by diffusion in the presence of a constant dividend. The integro expression of the Gerber-Shiu function is derivated by the strong markov property and also is continuous and twice continuously differentiable. then we obtain the integro-differential equation of the Gerber-Shiu function by formula, It is unique to research the ultimate ruin probability due to oscillation compared with other articles. Finally, we give the explicit expression of solution of integro-differential equation satisfied by when the claim sizes are exponential distribution.

Copyright

© 2014, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Leiping Jia
AU  - Yong Wu
AU  - Xiaoling Ma
AU  - Xiaoli Guo
PY  - 2014/11
DA  - 2014/11
TI  - Gerber-Shiu Function in the Compound Poisson Risk Model perturbed by diffusion under a Barrier Strategy
BT  - Proceedings of the 2014 International Conference on Mechatronics, Electronic, Industrial and Control Engineering
PB  - Atlantis Press
SP  - 225
EP  - 229
SN  - 2352-5401
UR  - https://doi.org/10.2991/meic-14.2014.51
DO  - 10.2991/meic-14.2014.51
ID  - Jia2014/11
ER  -