Optimal reinsurance subject to Vajda condition

Yichun Chi and Chengguo Weng

Insurance: Mathematics and Economics, 2013, vol. 53, issue 1, 179-189

Abstract: In this paper, we study optimal reinsurance design by minimizing the risk-adjusted value of an insurer’s liability, where the valuation is carried out by a cost-of-capital approach based either on the value at risk or the conditional value at risk. To prevent moral hazard and to be consistent with the spirit of reinsurance, we follow Vajda (1962) and assume that both the insurer’s retained loss and the proportion paid by a reinsurer are increasing in indemnity. We analyze the optimal solutions for a wide class of reinsurance premium principles which satisfy three axioms (law invariance, risk loading and preserving convex order) and encompass ten of the eleven widely used premium principles listed in Young (2004). Our results show that the optimal ceded loss functions are in the form of three interconnected line segments. Further simplified forms of the optimal reinsurance are obtained for the premium principles under an additional mild constraint. Finally, to illustrate the applicability of our results, we derive the optimal reinsurance explicitly for both the expected value principle and Wang’s principle.

Keywords: Cost of capital; Conditional value at risk; Value at risk; Optimal reinsurance; Vajda condition (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167668713000796
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:53:y:2013:i:1:p:179-189

DOI: 10.1016/j.insmatheco.2013.05.002

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().