Order Estimates for the Exact Lugannani-Rice Expansion

Takashi Kato, Jun Sekine and Kenichi Yoshikawa

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Abstract: The Lugannani-Rice formula is a saddlepoint approximation method for estimating the tail probability distribution function, which was originally studied for the sum of independent identically distributed random variables. Because of its tractability, the formula is now widely used in practical financial engineering as an approximation formula for the distribution of a (single) random variable. In this paper, the Lugannani-Rice approximation formula is derived for a general, parametrized sequence of random variables and the order estimates of the approximation are given.

Date: 2013-10, Revised 2014-06
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Published in Japan Journal of Industrial and Applied Mathematics, Vol.33(1), pp.25-61, 2016

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