Generating multivariate mixture of normal distributions using a modified Cholesky decomposition

Authors:
Jin Wang;Chunlei Liu
Affiliations:
Valdosta State University, Valdosta, GA;Valdosta State University, Valdosta, GA
Venue:
Proceedings of the 38th conference on Winter simulation
Year:
2006

Citing 3
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Modified Cholesky factorizations for sparse preconditioners

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Generating daily changes in market variables using a multivariate mixture of normal distributions

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Abstract

Mixture of normals is a more general and flexible distribution for modeling of daily changes in market variables with fat tails and skewness. An efficient analytical Monte Carlo method was proposed by Wang and Taaffe for generating daily changes using a multivariate mixture of normal distributions with arbitrary covariance matrix. However the usual Cholesky Decomposition will fail if the covariance matrix is not positive definite. In practice, the covariance matrix is unknown and has to be estimated. The estimated covariance may be not positive definite. We propose a modified Cholesky decomposition for semi-definite matrices and also suggest an optimal semi-definite approximation for indefinite matrices.