Pareto-optimal reinsurance policies in the presence of individual risk constraints

Lo, Ambrose; Tang, Zhaofeng

doi:10.1007/s10479-018-2820-4

Cited by 28 publications

(16 citation statements)

References 19 publications

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“…Remark 2.1. Similar to Cai et al (2017), if the premium principle satisfies semilinear: (γ Y + Z) = γ (Y ) + (Z) for any γ > 0 and Y , Z ∈ X , then all Pareto-optimal reinsurance treaties are included in the solutions to (2.2), see also Lo and Tang (2019) and Asimit et al (2020). However, the optimal solutions for CVaR risk measures in Cai et al (2017) may only belong to F but not belong to C. In order words, the method of constructing the optimal reinsurance treaties should be modified, and we should reconstruct the optimal solution.…”

Section: Preliminariesmentioning

confidence: 99%

“…A reinsurance is called to be Pareto-optimal if neither of the two parties can be better off without exasperating the other party. Lo and Tang (2019) further studied Pareto-optimal reinsurance design under distortion risk measures and gave explicit solutions to Pareto-optimal reinsurance treaty under VaR and CVaR risk measures and the expected value premium principle. For more works about optimal reinsurance from the perspectives of both the insurer and the reinsurer, we refer to Cheung and Wang (2017), Jiang et al (2017Jiang et al ( , 2018, Huang and Yin (2019), Asimit et al (2020), and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…As stated previously, the Vajda condition can reflect the spirit of reinsurance of protecting the insurer. The study of this paper can be regarded as a complement of those concerning Pareto-optimal reinsurance such as by Cai et al (2017) and Lo and Tang (2019). This paper can also be considered as a counterpart of Chi and Weng (2013) in the Pareto-optimal reinsurance setting.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Reinsurance From the Viewpoints of Both an Insurer and a Reinsurer Under the Cvar Risk Measure and Vajda Condition

Chen¹

2021

ASTIN Bull.

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In this paper, we study the optimal reinsurance contracts that minimize the convex combination of the Conditional Value-at-Risk (CVaR) of the insurer’s loss and the reinsurer’s loss over the class of ceded loss functions such that the retained loss function is increasing and the ceded loss function satisfies Vajda condition. Among a general class of reinsurance premium principles that satisfy the properties of risk loading and convex order preserving, the optimal solutions are obtained. Our results show that the optimal ceded loss functions are in the form of five interconnected segments for general reinsurance premium principles, and they can be further simplified to four interconnected segments if more properties are added to reinsurance premium principles. Finally, we derive optimal parameters for the expected value premium principle and give a numerical study to analyze the impact of the weighting factor on the optimal reinsurance.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Reinsurance From the Viewpoints of Both an Insurer and a Reinsurer Under the Cvar Risk Measure and Vajda Condition

Chen¹

2021

ASTIN Bull.

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“…Recently, Jiang et al (2017) and Cai et al (2016) solved the Pareto-optimal reinsurance when the insurer and reinsurer both measure the risk by using Value-at-Risk. Along this line, Lo and Tang (2018) investigated the problem by using the Neyman-Pearson approach and Cai et al (2017) solved the problem under the frame of Tail-Value-at-Risk. Lately, Jiang et al (2018) studied the Pareto-optimal reinsurance with constraints under distortion risk measures.…”

Section: Introductionmentioning

confidence: 99%

On the Optimal Risk Sharing in Reinsurance with Random Recovery Rate

2018

Risks

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This paper studies a Pareto-optimal reinsurance contract in the presence of negative statistical dependence between the insurance claim and the random recovery rate. In the context of symmetric information model and asymmetric information model, we investigate properties of the Pareto-optimal indemnity schedules. For risk neutral reinsurer with proportional cost and associated expense, we present possible forms of the Pareto-optimal indemnity schedule as well.Risks 2018, 6, 114 2 of 16 and uninsurable risks, Dana and Scarsini (2007) investigated qualitative properties of Pareto-optimal insurance contracts.Besides the additive one, the multiplicative background risk is quite common in the insurance practice. The counter-party risk in a reinsurance contract, which means the little chance that the reinsurer fails to pay the entire promised benefit to the insurer, is the default risk of the reinsurer. Readers may refer to Franke et al. (2006) for a comprehensive study on the multiplicative background risk. In the existing literature, researchers studied various characterizations of the counter-party risk together with its impact on the design of optimal reinsurance contract. For example, Tapiero et al. (1986) employed the perceived probability of ruin to characterize the probability of the insurer being affected by the reinsurer's default risk, and Schlesinger and Schulenburg (1987) considered a three-state model in which a loss that can not be indemnified occurs with a nonnegative probability, and discussed how insurance purchases are affected by the insurer's level of risk aversion. In the four-state model of Doherty and Schlesinger (1990), both the reinsurer and the insurer know the default probability, and the partial insurance is proved to be optimal when the reinsurer has a positive probability of total default. Later, such a result was extended to partial default by Mahul and Wright (2007). On the other hand, Cummins and Mahul (2003) derived the optimal insurance in the context that the reinsurer has a positive probability of total default and the reinsurer and insurer have divergent beliefs about this probability. Recently, Bernard and Ludkovski (2012) considered loss-dependent probability of default and partial recovery in the event of contract non-performance, and studied the Pareto-optimal reinsurance contracts with counter-party risk for risk neutral reinsurer and risk averse insurer. Thus, Bernard and Ludkovski (2012) extended the model of Dana and Scarsini (2007) to the case of multiplicative but not additive background risk.Usually, the background risk has significant impact on the Pareto-optimal reinsurance contract, and as is pointed out in Franke et al. (2006) and Bernard and Ludkovski (2012), the presence of multiplicative background risk can be more complex than the additive risk. On the other hand, in the presence of multiplicative background risk, Bernard and Ludkovski (2012) only dealt with binary recovery rate and risk neutral insurer with linear cost. In this study, we consider the reinsuranc...

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“…In many literature, to the perspective of the insurer, the optimal objective is usually assumed to maximize the expected utility of an insurer's terminal wealth, or to minimize the risk measure of an insurer's total retained risk. For example, see [3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,27,28,29,30,31,32] and the references therein.…”

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confidence: 99%

Optimal reinsurance with default risk: A reinsurer's perspective

Chen¹,

Liu²,

Tan³

et al. 2021

JIMO

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In this paper, we study the optimal reinsurance design with default risk by minimizing the VaR (value at risk) of the reinsurer's total risk exposure. The optimal reinsurance treaty is provided. When the reinsurance premium principle is specified to the expected value and exponential premium principles, the explicit expressions for the optimal reinsurance treaties are given, respectively.2020 Mathematics Subject Classification. 91B30. Key words and phrases. Optimal reinsurance, default risk, value at risk, expected value premium principle, exponential premium principle.

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Pareto-optimal reinsurance policies in the presence of individual risk constraints

Cited by 28 publications

References 19 publications

Optimal Reinsurance From the Viewpoints of Both an Insurer and a Reinsurer Under the Cvar Risk Measure and Vajda Condition

Optimal Reinsurance From the Viewpoints of Both an Insurer and a Reinsurer Under the Cvar Risk Measure and Vajda Condition

On the Optimal Risk Sharing in Reinsurance with Random Recovery Rate

Optimal reinsurance with default risk: A reinsurer's perspective

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