Marginal Indemnification Function formulation for optimal reinsurance

Zhuang, Sheng Chao; Weng, Chengguo; Tan, Ken Seng; Assa, Hirbod

doi:10.1016/j.insmatheco.2015.12.003

Cited by 91 publications

(56 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Technically, the 1-Lipschitz condition does result in some appealing mathematical convenience, with every f I and f R being absolutely continuous with derivatives f I and f R that exist almost everywhere and are bounded between 0 and 1. In line with Zhuang et al [19], we designate f I and f R as the marginal insurance indemnity function and the marginal reinsurance indemnity function, respectively, which measure the rate of increase in the insured loss with respect to the ground-up loss, and the rate of increase in the reinsured loss with respect to the insured loss. In addition to being handy equivalent representations of the optimal ( f I , f R ) due to the one-to-one correspondences…”

Section: Definition 1 (Definition Of Var)mentioning

confidence: 99%

See 1 more Smart Citation

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

2016

Risks

View full text Add to dashboard Cite

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.

show abstract

Section: Definition 1 (Definition Of Var)mentioning

confidence: 99%

“…Comparing the sum of Equations (18) and (19) to Equation (17), one observes that the change in the DRM of the risk exposure of the insurer is…”

Section: Corollary 1 (Extra Value Introduced By Reinsurance)mentioning

confidence: 99%

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

2016

Risks

View full text Add to dashboard Cite

show abstract

“…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%

“…As mathematical technique to solve the problems, we use the marginal indemnification function formulation as proposed by Assa [13] and Zhuang et al [16]. By means of this technique, these authors solve a reinsurance problem with homogeneous reference probabilities as originally solved by Cui et al [12].…”

Section: Introductionmentioning

confidence: 99%

“…By means of this technique, these authors solve a reinsurance problem with homogeneous reference probabilities as originally solved by Cui et al [12]. Zhuang et al [16] apply this technique to also solve a problem, where the insurer can only spend a maximum amount on reinsurance. In this paper, we propose this technique to solve a reinsurance problem with heterogeneous reference probabilities.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Reinsurance with Heterogeneous Reference Probabilities

Boonen

2016

Risks

View full text Add to dashboard Cite

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.

show abstract

References

2017

Reinsurance

View full text Add to dashboard Cite

Marginal Indemnification Function formulation for optimal reinsurance

Cited by 91 publications

References 26 publications

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

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

Optimal Reinsurance with Heterogeneous Reference Probabilities

References

Contact Info

Product

Resources

About