Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Stationary analysis of the surplus process in a risk model with investments

  • Lee, Eui Yong (Department of Statistics, Sookmyung Women's University)
  • Received : 2014.05.15
  • Accepted : 2014.06.24
  • Published : 2014.07.31
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Abstract

We consider a continuous time surplus process with investments the sizes of which are independent and identically distributed. It is assumed that an investment of the surplus to other business is made, if and only if the surplus reaches a given sufficient level. We establish an integro-differential equation for the distribution function of the surplus and solve the equation to obtain the moment generating function for the stationary distribution of the surplus. As a consequence, we obtain the first and second moments of the level of the surplus in an infinite horizon.

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References

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