# Optimal reinsurance under VaR and CTE risk measures

*Jun Cai*,
*Ken Seng Tan*,
*Chengguo Weng* and
*Yi Zhang*

*Insurance: Mathematics and Economics*, 2008, vol. 43, issue 1, 185-196

**Abstract:**
Let X denote the loss initially assumed by an insurer. In a reinsurance design, the insurer cedes part of its loss, say f(X), to a reinsurer, and thus the insurer retains a loss If(X)=X-f(X). In return, the insurer is obligated to compensate the reinsurer for undertaking the risk by paying the reinsurance premium. Hence, the sum of the retained loss and the reinsurance premium can be interpreted as the total cost of managing the risk in the presence of reinsurance. Based on a technique used in [Müller, A., Stoyan, D., 2002. Comparison Methods for Stochastic Models and Risks. In: Willey Series in Probability and Statistics] and motivated by [Cai J., Tan K.S., 2007. Optimal retention for a stop-loss reinsurance under the VaR and CTE risk measure. Astin Bull. 37 (1), 93-112] on using the value-at-risk (VaR) and the conditional tail expectation (CTE) of an insurer's total cost as the criteria for determining the optimal reinsurance, this paper derives the optimal ceded loss functions in a class of increasing convex ceded loss functions. The results indicate that depending on the risk measure's level of confidence and the safety loading for the reinsurance premium, the optimal reinsurance can be in the forms of stop-loss, quota-share, or change-loss.

**Date:** 2008

**References:** View references in EconPapers View complete reference list from CitEc

**Citations** View citations in EconPapers (38) Track citations by RSS feed

**Downloads:** (external link)

http://www.sciencedirect.com/science/article/pii/S0167-6687(08)00075-9

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:43:y:2008:i:1:p:185-196

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

Series data maintained by Dana Niculescu ().