The Gerber-Shiu discounted penalty function: A review from practical perspectives

Yue He, Reiichiro Kawai, Yasutaka Shimizu and Kazutoshi Yamazaki

Insurance: Mathematics and Economics, 2023, vol. 109, issue C, 1-28

Abstract: The Gerber-Shiu function provides a unified framework for the evaluation of a variety of risk quantities. Ever since its establishment, it has attracted constantly increasing interests in actuarial science, whereas the conventional research has been focused on finding analytical or semi-analytical solutions, either of which is rarely available, except for limited classes of penalty functions on rather simple risk models. In contrast to its great generality, the Gerber-Shiu function does not seem sufficiently prevalent in practice, largely due to a variety of difficulties in numerical approximation and statistical inference. To enhance research activities on such implementation aspects, we provide a comprehensive review of existing formulations and underlying surplus processes, as well as an extensive survey of analytical, semi-analytical and asymptotic methods for the Gerber-Shiu function, which altogether shed fresh light on its numerical methods and statistical inference for further developments. On the basis of an ambitious collection of 235 references, the present survey can serve as an insightful guidebook to model and method selection from practical perspectives as well.

Keywords: Gerber-Shiu function; Laplace transform; Integro-differential equations; Series expansions; Scale function (search for similar items in EconPapers)
JEL-codes: C14 C63 G22 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:109:y:2023:i:c:p:1-28

DOI: 10.1016/j.insmatheco.2022.12.003

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