Actuarial risk matrices : the nearest positive semidefinite matrix problem

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      <subfield code="a">Actuarial risk matrices</subfield>
      <subfield code="b">: the nearest positive semidefinite matrix problem</subfield>
      <subfield code="c">Stefan Cutajar, Helena Smigoc, Adrian O'Hagan</subfield>
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      <subfield code="a">The manner in which a group of insurance risks are interrelated is commonly presented via a correlation matrix. Actuarial risk correlation matrices are often constructed using output from disparate modeling sources and can be subjectively adjusted, for example, increasing the estimated correlation between two risk sources to confer reserving prudence. Hence, while individual elements still obey the assumptions of correlation values, the overall matrix is often not mathematically valid (not positive semidefinite). This can prove problematic in using the matrix in statistical models. The first objective of this article is to review existing techniques that address the nearest positive semidefinite matrix problem in a very general setting. The chief approaches studied are Semidefinite Programming (SDP) and the Alternating Projections Method (APM). </subfield>
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      <subfield code="g">04/12/2017 Tomo 21 Número 4 - 2017 , p. 552-564</subfield>
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