Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles
نویسندگان
چکیده
Recently the optimal reinsurance strategy concerning the insurer’s risk attitude and the reinsurance premium principle is an interesting topic. This paper discusses the optimal reinsurance problem with the insurer’s risk measured by distortion risk measure and the reinsurance premium calculated by a general principle including expected premium principle and Wang’s premium principle as its special cases. Explicit solutions of the optimal reinsurance strategy are obtained under the assumption that both the ceded loss and the retained loss are increasing with the initial loss. We present a new method for discussing the optimal problem. Based on our method, one can explain the optimal reinsurance treaty in the view of a balance between the insurer’s risk measure and the reinsurance premium principle. Key-words: Optimal reinsurance; Distortion risk measure; Reinsurance premium principle; Wang’s premium principle; VaR; TVaR. ∗Department of Financial Mathematics, Peking University, Beijing, 100871 †Department of Financial Mathematics, Center for Statistical Science, Peking University, Beijing, 100871, China. Email: [email protected] ‡Department of Financial Mathematics, Peking University, Beijing, 100871, China. Email: [email protected]
منابع مشابه
On Optimal Reinsurance Policy with Distortion Risk Measures and Premiums
In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by a distortion risk measure and the premium is given by a distortion risk premium. First, we show how the optimal reinsurance design for the ceding company, the reinsurance company and the social planner can be formulated in the same way. Second, by introducing the “marginal indemnification function...
متن کاملOptimal VaR-based risk management with reinsurance
It is well-known that reinsurance can be an effective risk management solution for financial institutions such as the insurance companies. The optimal reinsurance solution depends on a number of factors including the criterion of optimization and the premium principle adopted by the reinsurer. In this paper, we analyze the Value-at-Risk (VaR) based optimal risk management solution using reinsur...
متن کاملOptimal reinsurance under mean-variance premium principles
We derive optimal reinsurance under premium principles based on the mean and variance of the reinsurer’s share of the total claim amount. Both global reinsurance and local reinsurance are studied. Examples considered include standard deviation principle and variance principle. © 2001 Elsevier Science B.V. All rights reserved. MSC: Primary 90A46; Secondary 62P05
متن کاملOptimal Reinsurance under VaR and CTE Risk Measures
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 inter...
متن کاملOptimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account
Optimal forms of reinsurance policies have been studied for a long time in the actuarial literature. Most existing results are from the insurer’s point of view, aiming at maximizing the expected utility or minimizing the risk of the insurer. However, as pointed out by Borch (1969), it is understandable that a reinsurance arrangement that might be very attractive to one party (e.g., the insurer)...
متن کامل