Budget-Constrained Optimal Reinsurance Design Under Coherent Risk Measures

Cheung, Ka Chun; Chong, Wing Fung; Lo, Ambrose

doi:10.2139/ssrn.3077653

Cited by 3 publications

(4 citation statements)

References 26 publications

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“…These models then evolve to take account of more general risk measures, heterogeneous beliefs, incentive compatibility, and risk exposure constraints. See, for example, [4,20,21,23,27,33] for some of the most recent advances.…”

Section: Introductionmentioning

confidence: 99%

Pareto-optimal reinsurance with default risk and solvency regulation

Boonen

Jiang²

2023

Prob. Eng. Inf. Sci.

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This paper studies a Pareto-optimal reinsurance problem when the contract is subject to default of the reinsurer. We assume that the reinsurer can invest a share of its wealth in a risky asset and default occurs when the reinsurer's end-of-period wealth is insufficient to cover the indemnity. We show that without the solvency regulation, the optimal indemnity function is of excess-of-loss form, regardless of the investment decision. Under the solvency regulation constraint, by assuming the investment decision remains unchanged, the optimal indemnity function is characterized element-wisely. Partial results are derived when both the indemnity function and investment decision are impacted by the solvency regulation. Numerical examples are provided to illustrate the implications of our results and the sensitivity of solution to the model parameters.

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Section: Introductionmentioning

confidence: 99%

Pareto-optimal reinsurance with default risk and solvency regulation

Boonen

Jiang²

2023

Prob. Eng. Inf. Sci.

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“…Under various objective functions and premium principles and taking into account of more sophisticated economic factors, considerable advancements have been achieved in the literature. We refer to Chi and Tan (2011), Chi (2012), Cheung et al (2019), Ghossoub (2019b), Boonen and Ghossoub (2019) for recent developments.…”

Section: Introductionmentioning

confidence: 99%

Mean–variance Insurance Design With Counterparty Risk and Incentive Compatibility

Boonen¹,

Jiang

2021

ASTIN Bull.

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This paper studies the optimal insurance design from the perspective of an insured when there is possibility for the insurer to default on its promised indemnity. Default of the insurer leads to limited liability, and the promised indemnity is only partially recovered in case of a default. To alleviate the potential ex post moral hazard, an incentive compatibility condition is added to restrict the permissible indemnity function. Assuming that the premium is determined as a function of the expected coverage and under the mean–variance preference of the insured, we derive the explicit structure of the optimal indemnity function through the marginal indemnity function formulation of the problem. It is shown that the optimal indemnity function depends on the first and second order expectations of the random recovery rate conditioned on the realized insurable loss. The methodology and results in this article complement the literature regarding the optimal insurance subject to the default risk and provide new insights on problems of similar types.

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“…They studied unilateral optimal insurance problems via optimizing the buyer's variance and expected utility respectively. A vast literature has been readdressing their proposed unilateral optimal insurance problems via various objective functions in [6,11,14,16,17,20,31,32,34], premium principles in [12,15], practical constraints in [13,23,27,28,35,36,37], and more recently, heterogeneous beliefs in [7,18,24], as well as background risks in [19]; see also a recent work [22], and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…This paper revisits the optimal insurance contract design problem in terms of Pareto optimality. On one hand, we consider a premium budget constraint of the buyer; such a budget constraint has indeed been studied in unilateral optimal insurance design problems, such as Zheng and Cui (2014; [35]), Lo (2017;[27]), and Cheung et al (2019; [13]). On the other hand, this paper considers a minimum charge constraint for the seller; such a minimum charge constraint is well-justified for covering indirect costs of the seller due to the risk-transfer; this minimum charge is a fairly general lower bound of the premium payment that imposes a non-negative risk loading condition on the premium payment.…”

Section: Introductionmentioning

confidence: 99%