Centro de Documentacion de Fundación MAPFRE - Actuarial risk matrices : the nearest positive semidefinite matrix problem

MAP20180003967

Actuarial risk matrices : the nearest positive semidefinite matrix problem / Stefan Cutajar, Helena Smigoc, Adrian O'Hagan

Sumario: 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).

En: North American actuarial journal. - Schaumburg : Society of Actuaries, 1997- = ISSN 1092-0277. - 04/12/2017 Tomo 21 Número 4 - 2017 , p. 552-564

1. Matemática del seguro . 2. Cálculo actuarial . I. Smigoc, Helena . II. O'Hagan, Adrían . III. Título.