Optimal insurance under Wang’s premium principle

Young, Virginia R.

doi:10.1016/s0167-6687(99)00012-8

Cited by 141 publications

(77 citation statements)

References 10 publications

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“…Note that this set allows for deductible, or proportional reinsurance indemnities. The assumption that f ∈ F is often used in the literature on reinsurance contract design and its importance is particularly highlighted by Huberman et al [7], Denuit and Vermandele [21], and Young [9]. Non-increasing reinsurance indemnities are perceived to be undesirable as it encourages the insurer to underreport its losses.…”

Section: Modelmentioning

confidence: 99%

“…This model is extended later by many authors. 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

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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Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Reinsurance with Heterogeneous Reference Probabilities

Boonen

2016

Risks

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“…She assumes that the optimal insurance contract is of the co-insurance type and then looks for the optimal co-insurance factor. Young [19] and Bernard et al [20] examine a problem of optimal insurance design in which the insured is a rank-dependent expected utility maximizer [21,22]. Doherty and Eeckhoudt [23] study the optimal level of deductible under Yaari's dual theory [22].…”

Section: Related Literaturementioning

confidence: 99%

Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer

Amarante

Ghossoub

2016

Risks

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Abstract:In the classical expected utility framework, a problem of optimal insurance design with a premium constraint is equivalent to a problem of optimal insurance design with a minimum expected retention constraint. When the insurer has ambiguous beliefs represented by a non-additive probability measure, as in Schmeidler, this equivalence no longer holds. Recently, Amarante, Ghossoub and Phelps examined the problem of optimal insurance design with a premium constraint when the insurer has ambiguous beliefs. In particular, they showed that when the insurer is ambiguity-seeking, with a concave distortion of the insured's probability measure, then the optimal indemnity schedule is a state-contingent deductible schedule, in which the deductible depends on the state of the world only through the insurer's distortion function. In this paper, we examine the problem of optimal insurance design with a minimum expected retention constraint, in the case where the insurer is ambiguity-seeking. We obtain the aforementioned result of Amarante, Ghossoub and Phelps and the classical result of Arrow as special cases.

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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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Optimal insurance under Wang’s premium principle

Cited by 141 publications

References 10 publications

Optimal Reinsurance with Heterogeneous Reference Probabilities

Optimal Reinsurance with Heterogeneous Reference Probabilities

Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer

Optimal insurance in the presence of reinsurance

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