Characterizations of optimal reinsurance treaties: a cost-benefit approach

Cheung, Ka Chun; Lo, Ambrose

doi:10.1080/03461238.2015.1054303

Cited by 76 publications

(36 citation statements)

References 23 publications

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“…Moreover, we show that this approach can be used in case the insurer also faces costs of holding risk capital. For homogeneous reference probabilities, this problem is studied by Cheung and Lo [15]. Our result extends the setting to allow for heterogeneous reference probabilities, and the proof is much simpler.…”

Section: Introductionmentioning

confidence: 60%

“…The insurer is enforced hold risk capital given by ρĝ I (X − f (X), P I ) − E P I [X − f (X)], where ρĝ I (X − f (X), P I ),ĝ I ∈ G, is a distortion risk measure used to determine the risk capital is based on the probability measure P I . Such a valuation principle is used commonly in practice and is embedded in regulatory requirements under the Swiss Solvency Test and Solvency II (see, e.g., Chi [25], Asimit et al [26], and Cheung and Lo [15]). The wealth at a pre-determined future time for the insurer is given bŷ…”

Section: Costs Of Regulatory Capitalmentioning

confidence: 99%

“…For instance, Young [9] studies the case where the premium is given by Wang's premium principle. Moreover, Asimit et al [10], Chi and Tan [11], Cui et al [12], Assa [13], Balbás et al [14], Cheung and Lo [15], Zhuang et al [16]) all consider cases where the insurer minimizes a risk measure under a premium constraint.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Reinsurance with Heterogeneous Reference Probabilities

Boonen

2016

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This paper studies the problem of optimal reinsurance contract design. We let the insurer use dual utility, and the premium is an extended Wang's premium principle. The novel contribution is that we allow for heterogeneity in the beliefs regarding the underlying probability distribution. We characterize layer-reinsurance as an optimal reinsurance contract. Moreover, we characterize layer-reinsurance as optimal contracts when the insurer faces costs of holding regulatory capital. We illustrate this in cases where both firms use the Value-at-Risk or the conditional Value-at-Risk.

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Section: Introductionmentioning

confidence: 60%

Section: Costs Of Regulatory Capitalmentioning

confidence: 99%

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Optimal Reinsurance with Heterogeneous Reference Probabilities

Boonen

2016

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“…Despite their seemingly esoteric expressions, the optimal insurance-reinsurance decisions made by the insurer formulated in Theorem 1 are amenable to an instructive cost-benefit interpretation, which is an analogue of that in Cheung and Lo [12] in the classical insurer-reinsurer setting, and casts important light on the economic aspects of insurance and reinsurance. Such a cost-benefit perspective examines the gain and loss of insurance and reinsurance on a marginal loss basis and is highly conducive to understanding the structure of the optimal insurance-reinsurance strategies.…”

Section: Cost-benefit Interpretation Of Optimal Insurance-reinsurancementioning

confidence: 99%

“…The following auxiliary result, which can be found in Lemma 2.1 of Cheung and Lo [12], will prove handy when it comes to evaluating the DRM of a risk variable transformed by a non-decreasing, absolutely continuous function, of which a 1-Lipschitz function is a special case.…”

Section: Analytic Solutionsmentioning

confidence: 99%

How Does Reinsurance Create Value to an Insurer? A Cost-Benefit Analysis Incorporating Default Risk

2016

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Abstract:Reinsurance is often empirically hailed as a value-adding risk management strategy which an insurer can utilize to achieve various business objectives.In the context of a distortion-risk-measure-based three-party model incorporating a policyholder, insurer and reinsurer, this article formulates explicitly the optimal insurance-reinsurance strategies from the perspective of the insurer. Our analytic solutions are complemented by intuitive but scientifically rigorous explanations on the marginal cost and benefit considerations underlying the optimal insurance-reinsurance decisions. These cost-benefit discussions not only cast light on the economic motivations for an insurer to engage in insurance with the policyholder and in reinsurance with the reinsurer, but also mathematically formalize the value created by reinsurance with respect to stabilizing the loss portfolio and enlarging the underwriting capacity of an insurer. Our model also allows for the reinsurer's failure to deliver on its promised indemnity when the regulatory capital of the reinsurer is depleted by the reinsured loss. The reduction in the benefits of reinsurance to the insurer as a result of the reinsurer's default is quantified, and its influence on the optimal insurance-reinsurance policies analyzed.

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2017

Reinsurance

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Characterizations of optimal reinsurance treaties: a cost-benefit approach

Cited by 76 publications

References 23 publications

Optimal Reinsurance with Heterogeneous Reference Probabilities

Optimal Reinsurance with Heterogeneous Reference Probabilities

How Does Reinsurance Create Value to an Insurer? A Cost-Benefit Analysis Incorporating Default Risk

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