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Mathematical Problems in Engineering
Volume 2015, Article ID 143739, 12 pages
Research Article

Optimal Limited Stop-Loss Reinsurance under VaR, TVaR, and CTE Risk Measures

1China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, China
2Research Institute of Applied Mathematics, Anhua Agricultural Insurance Co., Ltd., Beijing 100037, China
3School of Economics and Management, Tsinghua University, Beijing 100084, China

Received 27 April 2015; Revised 14 July 2015; Accepted 15 July 2015

Academic Editor: Xinguang Zhang

Copyright © 2015 Xianhua Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper aims to provide a practical optimal reinsurance scheme under particular conditions, with the goal of minimizing total insurer risk. Excess of loss reinsurance is an essential part of the reinsurance market, but the concept of stop-loss reinsurance tends to be unpopular. We study the purchase arrangement of optimal reinsurance, under which the liability of reinsurers is limited by the excess of loss ratio, in order to generate a reinsurance scheme that is closer to reality. We explore the optimization of limited stop-loss reinsurance under three risk measures: value at risk (VaR), tail value at risk (TVaR), and conditional tail expectation (CTE). We analyze the topic from the following aspects: (1) finding the optimal franchise point with limited stop-loss coverage, (2) finding the optimal limited stop-loss coverage within a certain franchise point, and (3) finding the optimal franchise point with limited stop-loss coverage. We provide several numerical examples. Our results show the existence of optimal values and locations under the various constraint conditions.