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Journal of Statistical Theory and Practice

, Volume 6, Issue 2, pp 344–353 | Cite as

Further Results for the Joint Distribution of the Surplus Immediately Before and After Ruin Under Force of Interest

  • Kumer Pial Das
  • William Ted Mahavier
Article

Abstract

This article studies the joint distribution of the surplus immediately before ruin and the deficit at ruin under constant force of interest. A Laplace transformation technique has been used to establish an explicit expression for the joint distribution function with zero initial reserve. Numerical computation using this alternative expression is quick and easy in the case of exponential, gamma, and Pareto claim sizes. Moreover, a numerical method has been developed to efficiently approximate the joint distribution in case of nonzero initial reserve.

AMS Subject Classification

62P05 62E17 44A10 

Key-words

Compound Poisson model Laplace transformation Ruin probability Surplus process 

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Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  1. 1.Department of MathematicsLamar UniversityBeaumontUSA

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