The concept of comonotonicity in actuarial science and finance: theory. (English) Zbl 1051.62107

Dhaene, J.; Denuit, M.; Goovaerts, M. J.; Kaas, R.; Vyncke, D.

Insur. Math. Econ. 31, No. 1, 3-33 (2002).

Summary: In an insurance context, one is often interested in the distribution function of a sum of random variables. Such a sum appears when considering the aggregate claims of an insurance portfolio over a certain reference period. It also appears when considering discounted payments related to a single policy or a portfolio at different future points in time. The assumption of mutual independence between the components of the sum is very convenient from a computational point of view, but sometimes not realistic.
We determine approximations for sums of random variables, when the distributions of the terms are known, but the stochastic dependence structure between them is unknown or too cumbersome to work with. In this paper, the theoretical aspects are considered. Applications of this theory are considered in our subsequent paper, ibid., 133–161 (2002; Zbl 1037.62107). Both papers are to a large extent an overview of recent research results obtained by the authors, but also new theoretical and practical results are presented.

MSC:

62P05	Applications of statistics to actuarial sciences and financial mathematics
91B28	Finance etc. (MSC2000)
91B30	Risk theory, insurance (MSC2010)

Keywords:

Comonotonicity; Actuarial science and finance; Sums of random variables

Citations:

Zbl 1037.62107

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