Optimal reinsurance under VaR and CTE risk measures

Cai, Jun; Tan, Ken Seng; Weng, Chengguo; Zhang, Yi

doi:10.1016/j.insmatheco.2008.05.011

Cited by 205 publications

(152 citation statements)

References 13 publications

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“…These conditions are also assumed by [11,12], where they in fact require that f is Lipschitz-continuous (cf., e.g., Section 2 of [13]) and that f (x) linearly tends to infinity when x → ∞.…”

Section: Optimal Reinsurance Policies Whenmentioning

confidence: 99%

“…Borch [6] showed that for a fixed premium and expected reinsurance payments, the variance of the cedent's losses is minimized by the excess-of-loss reinsurance policy. In recent years, various solutions to the optimal reinsurance problem have been obtained where the value-at-risk (VaR) and the tail-value-at-risk (TVaR) have been used to measure the cedent's risk level (e.g., [7][8][9][10][11][12][13] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

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Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account

Jiang

Ren

Zitikis

2017

Risks

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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) can be quite unacceptable to the other party (e.g., the reinsurer). In this paper, we follow this point of view and study forms of Pareto-optimal reinsurance policies whereby one party's risk, measured by its value-at-risk (VaR), cannot be reduced without increasing the VaR of the counter-party in the reinsurance transaction. We show that the Pareto-optimal policies can be determined by minimizing linear combinations of the VaRs of the two parties in the reinsurance transaction. Consequently, we succeed in deriving user-friendly, closed-form, optimal reinsurance policies and their parameter values.

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Section: Optimal Reinsurance Policies Whenmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account

Jiang

Ren

Zitikis

2017

Risks

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“…., n. Actually, this is a particular framework strictly more restricted than that in Theorem 8, but this is a standard simplifica tion in the literature about the optimal reinsurance problem. See, for instance, Gajec and Zagrodny, 2004;Kaluszka, 2005;Cai et al, 2008, and many others, where the authors do not deal with the ori ginal probability space ðX; F; PÞ, but with its image R; B; P Ã ð Þby y 0 , composed of the real line R, the Borel r algebra B of R, and the probability measure P Ã given by P Ã ðBÞ Pðx 2 X; y 0 ðxÞ 2 BÞ for every Borel subset B 2 B. In such a particular case y 0 is replaced by the identity map.…”

Section: Algorithm and Numerical Experimentsmentioning

confidence: 99%

“…Along with the paper of Cai and Tan (2007) above, other interesting examples are Cai et al (2008), Balbás et al (2009) or Bernard and Tian (2009). The differ ences among their approaches are caused by the insurer behavior.…”

Section: Introductionmentioning

confidence: 99%

Stable solutions for optimal reinsurance problems involving risk measures

Balbás

Heras

2011

European Journal of Operational Research

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a b s t r a c tThe optimal reinsurance problem is a classic topic in actuarial mathematics. Recent approaches consider a coherent or expectation bounded risk measure and minimize the global risk of the ceding company under adequate constraints. However, there is no consensus about the risk measure that the insurer must use, since every risk measure presents advantages and shortcomings when compared with others.This paper deals with a discrete probability space and analyzes the stability of the optimal reinsurance with respect to the risk measure that the insurer uses. We will demonstrate that there is a ''stable optimal retention'' that will show no sensitivity, insofar as it will solve the optimal reinsurance problem for many risk measures, thus providing a very robust reinsurance plan. This stable optimal retention is a stop loss contract, and it is easy to compute in practice. A fast linear time algorithm will be given and a numerical example presented.

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“…See, for instance, Cai, et al [5], Chi [6] and Cheung, et al [7]. Recently, the optimization criterion of minimization of a number of ingenious risk measures is also widely applied, see Kaluszka [8,9], Gajek and Zagrodny [10], Promislow and Young [11], Cai, et al [12], Balbás, et al [13], Cheung [14], Chi and Weng [15] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle

Chen

Wang

Ming

2016

Risks

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Abstract:In this paper, we study the optimal reinsurance problem where risks of the insurer are measured by general law-invariant risk measures and premiums are calculated under the TVaR premium principle, which extends the work of the expected premium principle. Our objective is to characterize the optimal reinsurance strategy which minimizes the insurer's risk measure of its total loss. Our calculations show that the optimal reinsurance strategy is of the multi-layer form, i.e., f * (x) = x ∧ c * + (x − d * ) + with c * and d * being constants such that 0 ≤ c * ≤ d * .

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Optimal reinsurance under VaR and CTE risk measures

Cited by 205 publications

References 13 publications

Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account

Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account

Stable solutions for optimal reinsurance problems involving risk measures

Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle

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