Risk measures based on benchmark loss distributions

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<title>Risk measures based on benchmark loss distributions</title>
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<name type="personal" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20200010937">
<namePart>Burzoni, Matteo </namePart>
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<namePart>Munari, Cosimo </namePart>
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<abstract displayLabel="Summary">We introduce a class of quantile-based risk measures that generalize Value at Risk (VaR) and, likewise Expected Shortfall (ES), take into account both the frequency and the severity of losses. Under VaR a single confidence level is assigned regardless of the size of potential losses. We allow for a range of confidence levels that depend on the loss magnitude. The key ingredient is a benchmark loss distribution (BLD), that is, a function that associates to each potential loss a maximal acceptable probability of occurrence. The corresponding risk measure, called Loss VaR (LVaR), determines the minimal capital injection that is required to align the loss distribution of a risky position to the target BLD. By design, one has full flexibility in the choice of the BLD profile and, therefore, in the range of relevant quantiles. Special attention is given to piecewise constant functions and to tail distributions of benchmark random losses, in which case the acceptability condition imposed by the BLD boils down to first order stochastic dominance. We investigate the main theoretical properties of LVaR with a focus on their comparison with VaR and ES and discuss applications to capital adequacy, portfolio risk management, and catastrophic risk.</abstract>
<note type="statement of responsibility">Valeria Bignozzi, Matteo Burzoni, Cosimo Munari</note>
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<topic>Distribución de pérdidas</topic>
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<topic>Cálculo actuarial</topic>
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<topic>Valoración de riesgos</topic>
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<title>The Journal of risk and insurance</title>
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<publisher>Nueva York : The American Risk and Insurance Association, 1964-</publisher>
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<identifier type="issn">0022-4367</identifier>
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<text>01/06/2020 Volumen 87 Número 2 - junio 2020 , p. 437-475</text>
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