Optimal Reinsurance Under the Risk-Adjusted Value of an Insurer’s Liability and an Economic Reinsurance Premium Principle

Chi, Yichun; Lin, X. Sheldon; Tan, Ken Seng

doi:10.1080/10920277.2017.1302346

Cited by 18 publications

(18 citation statements)

References 31 publications

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“…Ratios of risk and expected surplus are related to risk-adjusted surplus under which many authors have examined how reinsurance could be optimized, see Chi (2012); Asimit et al (2013); Cheung and Lo (2017) and Chi et al (2017). Of particular significance for the present paper is Chi et al (2017) who were able to show that the reinsurance treaties maximizing risk-adjusted surplus are of the multi-layer type. It is not tenable to assume that reinsurance pricing is based on a fixed loading, as noted already by Borch (1960), and Chi et al (2017) made use of a general formulation of reinsurance pricing that goes back to Bühlmann (1980).…”

Section: Introductionmentioning

confidence: 74%

“…Of particular significance for the present paper is Chi et al (2017) who were able to show that the reinsurance treaties maximizing risk-adjusted surplus are of the multi-layer type. It is not tenable to assume that reinsurance pricing is based on a fixed loading, as noted already by Borch (1960), and Chi et al (2017) made use of a general formulation of reinsurance pricing that goes back to Bühlmann (1980). Many other researchers, for example, Chi and Tan (2013) and Zhuang et al (2016) have used this scheme.…”

Section: Introductionmentioning

confidence: 81%

“…That is how the insurance industry is regulated at present, but we shall argue that the perhaps theoretically more appealing Conditional Value at Risk could be handled in the same manner which would yield similar, but not quite identical results; see the companion paper Wang and Bølviken (2019). Ratios of risk and expected surplus are related to risk-adjusted surplus under which many authors have examined how reinsurance could be optimized, see Chi (2012); Asimit et al (2013); Cheung and Lo (2017) and Chi et al (2017). Of particular significance for the present paper is Chi et al (2017) who were able to show that the reinsurance treaties maximizing risk-adjusted surplus are of the multi-layer type.…”

Section: Introductionmentioning

confidence: 99%

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Optimal reinsurance for risk over surplus ratios

Bølviken¹,

Wang²

2019

Preprint

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Optimal reinsurance when Value at Risk and expected surplus is balanced through their ratio is studied, and it is demonstrated how results for risk-adjusted surplus can be utilized. Simplifications for large portfolios are derived, and this large-portfolio study suggests a new condition on the reinsurance pricing regime which is crucial for the results obtained. One or two layer contracts now become optimal for both risk-adjusted surplus and the risk over expected surplus ratio, but there is no second layer when portfolios are large or when reinsurance prices are below some threshold. Simple approximations of the optimum portfolio is considered, and their degree of degradation compared to the optimum is studied which leads to theoretical degradation rates as the number of policies grow. The theory is supported by numerical experiments which suggest that the shape of the claim severity distributions may not be of primary importance when designing an optimal reinsurance program. It is argued that the approach can be applied to Conditional Value at Risk as well.

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Section: Introductionmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

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Optimal reinsurance for risk over surplus ratios

Bølviken¹,

Wang²

2019

Preprint

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“…We can interpret the heterogeneous beliefs as the existence of different pricing kernels in the market. Therefore, we can also interpret this premium principle similarly to the one studied by Chi et al (2017) in the setting with one reinsurer, and preferences given by the risk-adjusted value of an insurer's liability.…”

Section: Expected Value Premium Principles With Heterogeneous Beliefsmentioning

confidence: 87%

On the existence of a representative reinsurer under heterogeneous beliefs

Boonen

Ghossoub

2019

Insurance: Mathematics and Economics

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This paper studies a one-period optimal reinsurance design model with n reinsurers and an insurer. The reinsurers are endowed with expected-value premium principles and with heterogeneous beliefs regarding the underlying distribution of the insurer's risk. Under general preferences for the insurer, a representative reinsurer is characterized. This means that all reinsurers can be treated collectively by means of a hypothetical premium principle in order to determine the optimal total risk that is ceded to all reinsurers. The optimal total ceded risk is then allocated to the reinsurers by means of an explicit solution. This is shown both in the general case and under the no-sabotage condition that avoids possible ex post moral hazard on the side of the insurer, thereby extending the results of Boonen et al. (2016). We subsequently derive closed-form optimal reinsurance contracts in case the insurer maximizes expected net wealth. Moreover, under the no-sabotage condition, we derive optimal reinsurance contracts in case the insurer maximizes dual utility, or in case the insurer maximizes a generic objective that preserves second-order stochastic dominance under the assumption of a monotone hazard ratio.

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“…In the framework of risk-averse utility functions, Arrow [2] established that such a stop-loss contract more generally maximizes the expected utility of the terminal wealth of the insurer. Over the following decades, there were many contributions in the field, generalizing these classical results for more intricate optimality criteria and/or more general premium principles (see for instance Gajek & Zagrodny [18], Kaluszka [22], Centeno & Guerra [20] as well as Tan et al [26], Malamud et al [25] and Chi et al [13] for some recent contributions, and [1,Ch.8] for a survey).…”

Section: Introductionmentioning

confidence: 99%

On randomized reinsurance contracts

Albrecher

Cani

2019

Insurance: Mathematics and Economics

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In this paper we discuss the potential of randomizing reinsurance treaties for efficient risk management. While it may be considered counter-intuitive to introduce additional external randomness in the determination of the retention function for a given occurred loss, we indicate why and to what extent randomizing a treaty can be interesting for the insurer. We illustrate the approach with a detailed analysis of the effects of randomizing a stop-loss treaty on the expected profit after reinsurance in the framework of a one-year reinsurance model under regulatory solvency constraints and cost of capital considerations.

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Optimal Reinsurance Under the Risk-Adjusted Value of an Insurer’s Liability and an Economic Reinsurance Premium Principle

Cited by 18 publications

References 31 publications

Optimal reinsurance for risk over surplus ratios

Optimal reinsurance for risk over surplus ratios

On the existence of a representative reinsurer under heterogeneous beliefs

On randomized reinsurance contracts

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