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Risks, Volume 1, Issue 2 (September 2013), Pages 45-80

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Research

Open AccessArticle Optimal Reinsurance: A Risk Sharing Approach
Risks 2013, 1(2), 45-56; doi:10.3390/risks1020045
Received: 11 June 2013 / Revised: 21 July 2013 / Accepted: 24 July 2013 / Published: 5 August 2013
Cited by 2 | PDF Full-text (205 KB) | HTML Full-text | XML Full-text
Abstract
This paper proposes risk sharing strategies, which allow insurers to cooperate and diversify non-systemic risk. We deal with both deviation measures and coherent risk measures and provide general mathematical methods applying to optimize them all. Numerical examples are given in order to [...] Read more.
This paper proposes risk sharing strategies, which allow insurers to cooperate and diversify non-systemic risk. We deal with both deviation measures and coherent risk measures and provide general mathematical methods applying to optimize them all. Numerical examples are given in order to illustrate how efficiently the non-systemic risk can be diversified and how effective the presented mathematical tools may be. It is also illustrated how the existence of huge disasters may lead to wrong solutions of our optimal risk sharing problem, in the sense that the involved risk measure could ignore the existence of a non-null probability of "global ruin" after the design of the optimal risk sharing strategy. To overcome this caveat, one can use more conservative risk measures. The stability in the large of the optimal sharing plan guarantees that "the global ruin caveat" may be also addressed and solved with the presented methods. Full article
(This article belongs to the collection Systemic Risk and Reinsurance)
Open AccessArticle A Welfare Analysis of Capital Insurance
Risks 2013, 1(2), 57-80; doi:10.3390/risks1020057
Received: 26 July 2013 / Revised: 29 August 2013 / Accepted: 6 September 2013 / Published: 17 September 2013
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Abstract
This paper presents a welfare analysis of several capital insurance programs in a rational expectation equilibrium setting. We first explicitly characterize the equilibrium of each capital insurance program. Then, we demonstrate that a capital insurance program based on aggregate loss is better [...] Read more.
This paper presents a welfare analysis of several capital insurance programs in a rational expectation equilibrium setting. We first explicitly characterize the equilibrium of each capital insurance program. Then, we demonstrate that a capital insurance program based on aggregate loss is better than classical insurance, when big financial institutions have similar expected loss exposures. By contrast, classical insurance is more desirable when the bank’s individual risk is consistent with the expected loss in a precise way. Our analysis shows that a capital insurance program is a useful tool to hedge systemic risk from the regulatory perspective. Full article
(This article belongs to the collection Systemic Risk and Reinsurance)

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