Asymptotic theory for the empirical Haezendonck-Goovaerts risk measure

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      <subfield code="a">Ahn, Jae Youn</subfield>
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      <subfield code="a">Asymptotic theory for the empirical Haezendonck-Goovaerts risk measure</subfield>
      <subfield code="c">Jae Youn Ahn, Nariankadu D. Shyamalkumar</subfield>
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      <subfield code="a">HaezendonckGoovaerts risk measures is a recently introduced class of risk measures which includes, as its minimal member, the Tail Value-at-Risk (T-VaR)T-VaR arguably the most popular risk measure in global insurance regulation. In applications often one has to estimate the risk measure given a random sample from an unknown distribution. The distribution could either be truly unknown or could be the distribution of a complex function of economic and idiosyncratic variables with the complexity of the function rendering indeterminable its distribution. Hence statistical procedures for the estimation of HaezendonckGoovaerts risk measures are a key requirement for their use in practice. A natural estimator of the HaezendonckGoovaerts risk measure is the HaezendonckGoovaerts risk measure of the empirical distribution, but its statistical properties have not yet been explored in detail. The main goal of this article is to both establish the strong consistency of this estimator and to derive weak convergence limits for this estimator. We also conduct a simulation study to lend insight into the sample sizes required for these asymptotic limits to take hold.</subfield>
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      <subfield code="t">Insurance : mathematics and economics</subfield>
      <subfield code="d">Oxford : Elsevier, 1990-</subfield>
      <subfield code="x">0167-6687</subfield>
      <subfield code="g">03/03/2014 Volumen 55 Número 1 - marzo 2014 </subfield>
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