Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (3): 677-693.

• Articles • Previous Articles     Next Articles

Joint Distributions of Some Actuarial Random Vectors in the Continuous-time Compound Binomial Model

 ZHAO Jin-Yan1, LIU Guo-Xin2   

  1. 1.School of Mathematical Science and Computing Technology, Central South University, Changsha 410075;
    2.School of Science, Hebei University of Technology, Tianjin 300130
  • Received:2008-06-12 Revised:2009-11-05 Online:2010-05-25 Published:2010-05-25
  • Supported by:

    国家自然科学基金(10671052)资助

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Abstract:

The continuous-time compound binomial model, firstly proposed by[1], is the continuous-time version of the compound binomial model.
In this paper, a renewal mass function of a defective renewal sequence constituted by the up-crossing zero points is introduced in the continuous-time compound binomial model. By the mass function together with the strong Markov property of the surplus process X(t), the explicit expressions of the ruin probability and the joint distributions of some actuarial random vectors such as (T, X(T-), |X(T)|), (T, X(T-), |X(T)|, inf0≤t<L X(t)) and (T, X(T-), |X(T)|, sup0≤t<T X(t)) are obtained, where T represents the time of ruin and L the time of the surplus process leaving deficit ultimately. The corresponding joint distributions are directly obtained for the compound binomial model, {X(n)}, as the 1-skeleton chain of the continuous-time compound binomial model. Finally, a special case with the claim amount being geometrically distributed in the compound binomial model is considered.

Key words: Joint distribution, Continuous-time compound binomial model, Renewal mass function, Sequence of up-crossing zero points, Ruin probability

CLC Number: 

  • 60K10
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