Some new results on allocation of coverage limits and deductibles to mutually independent risks

ABSTRACT

This article further investigates the allocation of coverage limits and deductibles to multiple independent risks from the viewpoint of policyholders with increasing utility functions. In a more general setup, we develop the usual stochastic orders on the retained loss, which either generalize or supplement the corresponding results due to Lu and Meng (2011) and Hu and Wang (2014). Also, the most unfavorable and favorable allocations of coverage limits and deductibles are developed for multiple risks with dominated reversed hazard rates and hazard rates, respectively.

KEYWORDS:

• DRHR
• IHR
• Majorization
• Reversed hazard rate order.

Mathematics Subject Classification:

• Primary 91B16, 91B30
• Secondary 60E15

Acknowledgments

The authors would like to thank the two anonymous referees for their insightful comments, which have helped greatly improve the presentation of this article.