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Solvency II, regulatory capital, and optimal reinsurance : How good are Conditional Value-at-Risk and spectral risk measures?

 
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<title>Solvency II, regulatory capital, and optimal reinsurance</title>
<subTitle>: How good are Conditional Value-at-Risk and spectral risk measures?</subTitle>
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<namePart>Brandtner, Mario</namePart>
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<namePart>Kürsten, Wolfgang</namePart>
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<abstract displayLabel="Summary">We study the problem of optimal reinsurance as a means of risk management in the regulatory framework of Solvency II under Conditional Value-at-Risk and, as its natural extension, spectral risk measures. First, we show that stop-loss reinsurance is optimal under both Conditional Value-at-Risk and spectral risk measures. Spectral risk measures thus constitute a more general class of suitable regulatory risk measures than specific Conditional Value-at-Risk. At the same time, the established type of stop-loss reinsurance can be maintained as the optimal risk management strategy that minimizes regulatory capital. Second, we derive the optimal deductibles for stop-loss reinsurance. We show that under Conditional Value-at-Risk, the optimal deductible tends towards restrictive and counter-intuitive corner solutions or plunging, which is a serious objection against its use in regulatory risk management. By means of the broader class of spectral risk measures, we are able to overcome this shortcoming as optimal deductibles are now interior solutions. Especially, the recently discussed power spectral risk measures and the Wang risk measure are shown to avoid any plunging. They yield a one-to-one correspondence between the risk parameter and the optimal deductible and, thus, provide economically plausible risk management strategies.</abstract>
<note type="statement of responsibility">Mario Brandtner,  Wolfgang Kürsten</note>
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<topic>Matemática del seguro</topic>
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<topic>Cálculo actuarial</topic>
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<topic>Métodos de optimización</topic>
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<topic>Gerencia de riesgos</topic>
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<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080564254">
<topic>Solvencia II</topic>
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<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080594664">
<topic>Análisis espectrales</topic>
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<topic>Deductibles</topic>
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<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080604394">
<topic>Valoración de riesgos</topic>
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<title>Insurance : mathematics and economics</title>
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<publisher>Oxford : Elsevier, 1990-</publisher>
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<identifier type="issn">0167-6687</identifier>
<identifier type="local">MAP20077100574</identifier>
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<text>03/11/2014 Volumen 59 Número 1 - noviembre 2014 , p. 156-167</text>
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