On a dual model with a dividend threshold
In insurance mathematics, a compound Poisson model is often used to describe the aggregate claims of the surplus process. In this paper, we consider the dual of the compound Poisson model under a threshold dividend strategy. We derive a set of two integrodifferential equations satisfied by the expected total discounted dividends until ruin and show how the equations can be solved by using only one of the two integrodifferential equations. The cases where profits follow an exponential or a mixture of exponential distributions are then solved and the discussion for the case of a general profit distribution follows by the use of Laplace transforms. We illustrate how the optimal threshold level that maximizes the expected total discounted dividends until ruin can be obtained, and finally we generalize the results to the case where the surplus process is a more general skipfree downwards Lévy process.
Year of publication: 
2009


Authors:  Ng, Andrew C.Y. 
Published in: 
Insurance: Mathematics and Economics.  Elsevier, ISSN 01676687.  Vol. 44.2009, 2, p. 315324

Publisher: 
Elsevier 
Keywords:  Ruin theory Dual risk model Threshold strategy Optimal threshold problem 
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