Journal of Guangxi Normal University(Natural Science Edition) ›› 2011, Vol. 29 ›› Issue (3): 23-27.

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Gerber-Shiu Function of MAP Risk Process Perturbedby Diffusion

TANG Sheng-da, QIN Yong-song   

  1. College of Mathematical Science,Guangxi Normal University,Guilin Guangxi 541004,China
  • Received:2011-04-29 Online:2011-08-20 Published:2018-12-03

Abstract: A risk model perturbed by diffusion is proposed in this paper.Claims arrival belongs to markovian arrival process (MAP).The integro-differential equations satisfied by Laplace transform of the Gerber-Shiu functions and closed form of expression for the Gerber-Shiu functions are obtained through divided difference and Dickson-Hipp operator when the claim amount distribution is from the rational family.Finally,in order to illustrate the main results,a numerical example is provided.

Key words: risk theory, Gerber-Shiu function, MAP, Integro-differential equation, Laplace transform

CLC Number: 

  • O211.9
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