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Some problems in finite dams with an application to insurance risk

  • B. Weesakul
  • G. F. Yeo
Article

Summary

This paper considers a finite dam in continuous time fed by inputs, with a negative exponential distribution, whose arrival times form a Poisson process; there is a continuous release at unit rate, and overflow is allowed. Various results have been obtained by appropriate limiting methods from an analogous discrete time process, for which it is possible to find some solutions directly by determinantal methods.

First the stationary dam content distribution is found. The distribution of the probability of first emptiness is obtained both when overflow is, and is not allowed. This is followed by the probability the overflow before emptiness, which is then applied to determine the exact solution for an insurance risk problem with claims having a negative exponential distribution. The time-dependent content distribution is found, and the analogy with queueing theory is discussed.

Keywords

Exact Solution Arrival Time Time Process Stochastic Process Discrete Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1963

Authors and Affiliations

  • B. Weesakul
    • 1
    • 2
  • G. F. Yeo
    • 1
    • 2
  1. 1.National Statistical OfficesBangkok
  2. 2.Department of MathematicsStanford UniversityStanford

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