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Optimal dividends with incomplete information in the dual model. (English) Zbl 1189.91074
Summary: In [H. U. Gerber, E. S. W. Shiu and N. Smith, Insur. Math. Econ. 42, No. 1, 243–254 (2008; Zbl 1141.91513)], methods were analyzed for estimating the optimal dividend barrier (in the sense of de Finetti). In particular, De Vylder approximations and diffusion approximations are discussed. These methods are useful when only the first few moments of the claim amount distribution are known. The purpose of this paper is to examine these and other methods (such as the gamma approximations and the gamproc approximations) in the dual model, see [B. Avanzi, H. U. Gerber and E. S. W. Shiu, Insur. Math. Econ. 41, No. 1, 111–123 (2007; Zbl 1131.91026)]. The dual model is obtained if the roles of premiums and claims are exchanged. In other words, the company has random gains, which constitute a compound Poisson process, and expenses occur continuously at a constant rate. The approximations can easily be implemented, and their accuracy is surprisingly good. Several numerical illustrations enhance the paper.

91B30 Risk theory, insurance (MSC2010)
Full Text: DOI
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