Convex Ordering for Insurance Preferences

24 Pages Posted: 23 Apr 2015 Last revised: 26 Aug 2015

See all articles by Ka Chun Cheung

Ka Chun Cheung

The University of Hong Kong

Wing Fung Chong

Heriot-Watt University - Department of Actuarial Mathematics and Statistics

S. C. P. Yam

The Chinese University of Hong Kong. Department of Statistics

Date Written: June 1, 2015

Abstract

In this article, we study two broad classes of convex order related optimal insurance decision problems, in which the objective function or the premium valuation is a general functional of the expectation, Value-at-Risk and Average Value-at-Risk of the loss variables. These two classes of problems include many existing and contemporary optimal insurance problems as interesting examples being prevalent in the literature. To solve these problems, we apply the Karlin-Novikoff-Stoyan-Taylor multiple-crossing conditions, which is a useful sufficient criterion in the theory of convex ordering, to replace an arbitrary insurance indemnity by a more favorable one in convex order sense. The convex ordering established provide a unifying approach to solve the special cases of the problem classes. We show that the optimal indemnities for these problems in general take the double layer form.

Keywords: Convex ordering, Karlin-Novikoff-Stoyan-Taylor crossing conditions, Value-at-Risk, Average Value-at-Risk, Optimal insurance decision problem

Suggested Citation

Cheung, Ka Chun and Chong, Wing Fung and Yam, Phillip, Convex Ordering for Insurance Preferences (June 1, 2015). Insurance: Mathematics and Economics, 64:409-416, Available at SSRN: https://ssrn.com/abstract=2597929 or http://dx.doi.org/10.2139/ssrn.2597929

Ka Chun Cheung (Contact Author)

The University of Hong Kong ( email )

Pokfulam Road
Hong Kong, Pokfulam HK
China

Wing Fung Chong

Heriot-Watt University - Department of Actuarial Mathematics and Statistics ( email )

Edinburgh, Scotland EH14 4AS
United Kingdom

Phillip Yam

The Chinese University of Hong Kong. Department of Statistics ( email )

Hong Kong

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