On optimal reinsurance policy with distortion risk measures and premiums

Assa, Hirbod

doi:10.1016/j.insmatheco.2014.11.007

Cited by 80 publications

(35 citation statements)

References 21 publications

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“…If there is only one reinsurer and the insurer maximizes dual utility (Yaari, 1987), the optimal reinsurance contract is given by tranching of the total insurance risk as shown by Assa (2015). We extend this result to the case of the presence of multiple reinsurers.…”

Section: Introductionmentioning

confidence: 86%

“…In contrast to Assa (2015), we solve the optimal reinsurance problem in the context of multiple reinsurers. Moreover, we show that under mild conditions, the optimal reinsurance contracts are Lipschitz as assumed by Assa (2015). The distortion risk measure used by the insurer might be generated by any non-decreasing distortion function, especially the inverse-S shaped distortion function which has recently gained popularity in behavioral finance (see Section 5).…”

Section: Special Case: Preferences Given By Dual Utilitymentioning

confidence: 99%

“…In fact, our premium principle is quite general in that we assume the reinsurers use distortion premium principles. Many authors, including Wang (1995Wang ( , 2000, Wang et al (1997), De Waegenaere et al (2003), Chen and Kulperger (2006), Cheung (2010) and Assa (2015), use distortion functions to price risk. Special cases include the pricing principle induced by a Wang transform, Value-at-Risk, and expected value principle.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Reinsurance with One Insurer and Multiple Reinsurers

2015

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In this paper, we consider a one-period optimal reinsurance design model with n reinsurers and an insurer. For very general preferences of the insurer, we obtain that there exists a very intuitive pricing formula for all reinsurers that use a distortion premium principle. The insurer determines its optimal risk that it wants to reinsure via this pricing formula. This risk it wants to reinsure is then shared by the reinsurers via tranching. The optimal ceded loss functions among multiple reinsurers are derived explicitly under the additional assumptions that the insurer's preferences are given by an inverse-S shaped distortion risk measure and that the reinsurer's premium principles are some functions of the Conditional Value-at-Risk. We also demonstrate that under some prescribed conditions, it is never optimal for the insurer to cede its risk to more than two reinsurers.

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Section: Introductionmentioning

confidence: 86%

Section: Special Case: Preferences Given By Dual Utilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Reinsurance with One Insurer and Multiple Reinsurers

2015

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“…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%

Optimal Reinsurance with Heterogeneous Reference Probabilities

Boonen

2016

Risks

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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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“…These pioneering results are later extended to situation where there is a more sophisticated objective function and/or more realistic premium principles (see, e.g. Young 1999, Gajek & Zagrodny 2000, 2004, Kaluszka 2001, 2005, Cai & Tan 2007, Balbás et al 2009, 2015, Chi 2012, Asimit et al 2013, 2015, Cai et al 2013, Forthcoming, Chi & Tan 2013, Cui et al 2013, Cheung et al 2014, 2015, Bernard et al 2015, Cheung et al 2015, Boonen et al 2016. In the above-mentioned papers, the risk of the insurer is typically given and the objective boils down to determining an optimal strategy of transferring part of its risk to a reinsurer.…”

Section: Introductionmentioning

confidence: 99%

Optimal insurance in the presence of reinsurance

Zhuang

Boonen

Tan

et al. 2016

Scandinavian Actuarial Journal

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This paper studies an optimal insurance and reinsurance design problem among three agents: policyholder, insurer, and reinsurer. We assume that the preferences of the parties are given by distortion risk measures, which are equivalent to dual utilities. By maximizing the dual utility of the insurer and jointly solving the optimal insurance and reinsurance contracts, it is found that a layering insurance is optimal, with every layer being borne by one of the three agents. We also show that reinsurance encourages more insurance, and is welfare improving for the economy. Furthermore, it is optimal for the insurer to charge the maximum acceptable insurance premium to the policyholder. This paper also considers three other variants of the optimal insurance/reinsurance models. The first two variants impose a limit on the reinsurance premium so as to prevent insurer to reinsure all its risk. An optimal solution is still layering insurance, though the insurer will have to retain higher risk. Finally, we study the effect of competition by permitting the policyholder to insure its risk with an insurer, a reinsurer, or both. The competition from the reinsurer dampens the price at which an insurer could charge to the policyholder, although the optimal indemnities remain the same as the baseline model. The reinsurer will however not trade with the policyholder in this optimal solution. ARTICLE HISTORY

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On optimal reinsurance policy with distortion risk measures and premiums

Cited by 80 publications

References 21 publications

Optimal Reinsurance with One Insurer and Multiple Reinsurers

Optimal Reinsurance with One Insurer and Multiple Reinsurers

Optimal Reinsurance with Heterogeneous Reference Probabilities

Optimal insurance in the presence of reinsurance

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