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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Lamar University, Beaumont, TX, 77710, USA

    Kumer Pial Das & William Ted Mahavier

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  1. Kumer Pial Das
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  2. William Ted Mahavier
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Correspondence to Kumer Pial Das.

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Das, K.P., Mahavier, W.T. Further Results for the Joint Distribution of the Surplus Immediately Before and After Ruin Under Force of Interest. J Stat Theory Pract 6, 344–353 (2012). https://doi.org/10.1080/15598608.2012.673895

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  • DOI: https://doi.org/10.1080/15598608.2012.673895

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