Optimal insurance under the insurer’s risk constraint

Zhou, Chunyang; Wu, Chongfeng

doi:10.1016/j.insmatheco.2007.11.005

Cited by 35 publications

(25 citation statements)

References 17 publications

(23 reference statements)

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“…As shown in Zhou and Wu (2008), for instance, when the insurer implements the expected shortfall requirements, the insured's optimal indemnity is a capped deductible (clearly, it is continuous). 14 The expected shortfall requirement might be attractive for the insurer, as the indemnity is capped.…”

Section: Discussionmentioning

confidence: 99%

“…A similar problem has recently been solved by Zhou and Wu (2008). The latter study considers a regulatory constraint on the expected tail risk instead of the probability of the tail risk.…”

Section: Previous Literaturementioning

confidence: 99%

“…Note that a constraint on the expected shortfall is a convex-style constraint and standard techniques can be employed. We will compare the optimal contract solving Problem 2.2 with the contract in Zhou and Wu (2008) in the section ''Optimal design for the insured''. In another recent paper, Huang (2006) considers the optimal contract for the insured under the following constraint:…”

Section: Previous Literaturementioning

confidence: 99%

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Insurance Market Effects of Risk Management Metrics

Bernard

Tian

2010

Geneva Risk Insur Rev

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We extend the classical analysis on optimal insurance design to the case when the insurer implements regulatory requirements (Value-at-Risk). Presumably, regulators impose some risk management requirement such as VaR to reduce the insurers' insolvency risk, as well as to improve the insurance market stability. We show that VaR requirements may better protect the insured and improve economic efficiency, but have stringent negative effects on the insurance market. Our analysis reveals that the insured are better protected in the event of greater loss irrespective of the optimal design from either the insured or the insurer perspective. However, in the presence of the VaR requirement on the insurer, the insurer's insolvency risk might be increased and there are moral hazard issues in the insurance market because the optimal contract is discontinuous. IntroductionThis paper shows that Value-at-Risk (VaR) regulatory requirements have controversial effects on the insurance market. On the one hand, the insured are better protected in the event of a large loss irrespective of the optimal design from either the insured's or the issuer's side, when the insurer implements VaR imposed by regulators. On the other hand, since the insurer then covers more, when a large loss occurs, the default risk of the insurer is increased, as well as the instability of the market. Moreover, because of the presence of discontinuities in the optimal insurance contract presented in this paper, the optimal risk sharing introduces moral hazard issues in the insurance market.The Geneva Risk and Insurance Review, 2010, 35, (47-80) r 2010 The International Association for the Study of Insurance Economics 1554-964X/10 www.palgrave-journals.com/grir/ VaR is not a new concept in risk management. Recommendations on banking laws and regulations issued by the Basel Committee on Banking Supervision have been implemented in the banking sector. In Basel I and Basel II, the VaR methodology is used to deal with the market risk and the credit risk. Similarly, in Solvency II 1 for the insurance sector, the economic capital could be calculated by an internal VaR model. However, whether VaR risk management 2 requirements really enhance the efficiency and stability of the market still remains elusive. For instance, in the context of financial market, Basak and Shapiro (2001) derive that the presence of VaR risk managers amplifies the stock-market volatility in a downward market and attenuates the volatility in an upward market. The 2007-2008 global financial crises lead to even more serious concerns on the adequacy of VaR methodology to deal with credit risk. This paper reveals some negative aspects of the regulatory VaR methodology in the insurance market.We develop a theoretical framework to investigate the economic consequences for the insured and to the insurance market in the presence of regulatory risk management requirements on insurers. This study is done under the expected utility paradigm and the risk management requirement is interpreted as a VaR c...

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Section: Discussionmentioning

confidence: 99%

“…A similar problem has recently been solved by Zhou and Wu (2008). The latter study considers a regulatory constraint on the expected tail risk instead of the probability of the tail risk.…”

Section: Previous Literaturementioning

confidence: 99%

Section: Previous Literaturementioning

confidence: 99%

See 1 more Smart Citation

Insurance Market Effects of Risk Management Metrics

Bernard

Tian

2010

Geneva Risk Insur Rev

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“…Wang et al (2005) and Huang (2006) consider the problem of optimal insurance under the constraint of insurer's VaR risk, calculating the deductible form of optimal insurance. Zhou and Wu (2008) impose the insurer's risk constraint on Arrow's optimal insurance model. They consider the problem of optimal insurance under the expected utility criterion, discussing the deductible form of optimal insurance.…”

Section: Introductionmentioning

confidence: 99%

On the optimal design of insurance contracts with the restriction of equity risk

Sun

Dong

2015

Economic Modelling

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“…Other related contributions include Zagrodny (2000, 2004), Promislow and Young (2005), Balbás et al (2009) and the references therein. Recent relevant papers on the expected utility maximization models include Zhou and Wu (2008) and Zhou et al (2010). 1 More recently, two important risk measures known as the Value-at-Risk (VaR) and the conditional tail expectation (CTE) have 1 Both papers analyze the optimal insurance purchase, but their results could be applied to the optimal reinsurance purchase.…”

Section: Introductionmentioning

confidence: 99%