083010 (M10, M12) Stop-loss bounds for diatomic bivariate sums by given marginal means, variances and positive correlation : Hürlimann W., XXVII Astin Colloquium, Copenhagen, Denmark, 1996, volume 1, pp. 626 – 633
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 89 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0167-6687
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✦ Synopsis
A structure of financial loss on probability space is considered. The financial loss is represented as difference between loss and gain. In this general mathematical framework, the inequality of Bowers (1969) on the mean loss, as well as inequalities by Kremer (1990), H0rlimann (1993 a/b) on the loss variance, are all simple consequences of the nonnegative property of certain variance functions. Similar inequalities for the gain are obtained via a conjugate operation. Sharpness and extremal properties of the variance bounds are discussed. By given mean, variance of the financial loss, and fixed mean loss, it is shown that the loss and gain variance extremal bounds are attained for diatomic financial losses. In the special case of the stop-loss variance upper bond, this results is originally due to Schmitter (1993Schmitter ( /1995)). The potential usefulness of our approach for asset and liability management, including in particular some actuarial hedging models, is briefly mentioned.