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

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