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Title: Higher order saddlepoint approximations Authors:  Raymond Kan - University of Toronto (Canada) [presenting]
Simon Broda - University of Amsterdam (Netherlands)
Abstract: Higher order saddlepoint approximations are presented for the density and cumulative distribution function of univariate and multivariate random variables. While the results of higher order saddlepoint approximations for the univariate case are generally known, the corresponding results for the multivariate case are largely missing in the literature. In addition, existing results on multivariate saddlepoint approximations are quite cumbersome to use. As a result, we see very few applications that make use of saddlepoint approximations for the multivariate case. Overcoming this problem, we present simple recursive algorithms that facilitate the computation of higher order terms for the saddlepoint approximation. A number of numerical examples are given to illustrate the potential benefit of using higher order saddlepoint approximations.