Frontiers of Mathematics in China >
Saddlepoint approximation for moments of random variables
Received date: 15 Oct 2010
Accepted date: 10 Mar 2011
Published date: 01 Dec 2011
Copyright
In this paper, we introduce a saddlepoint approximation method for higher-order moments like , a>0, where the random variable S in these expectations could be a single random variable as well as the average or sum of some i.i.d random variables, and a>0 is a constant. Numerical results are given to show the accuracy of this approximation method.
Kai ZHAO , Xue CHENG , Jingping YANG . Saddlepoint approximation for moments of random variables[J]. Frontiers of Mathematics in China, 2011 , 6(6) : 1265 -1284 . DOI: 10.1007/s11464-011-0128-7
1 |
Barndorff-Nielsen O, Cox D R. Edgeworth and saddle-point approximations with statistical applications. J R Statist Soc B, 1979, 41(3): 279-312
|
2 |
Butler R W. Saddle-point Approximations with Applications. Cambridge: Cambridge University Press, 2007
|
3 |
Daniels H E. Saddlepoint approximations in statistics. Ann Math Statist, 1954, 25: 631-650
|
4 |
Daniels H E. Tail probability approximations. Internat Statist Rev, 1987, 55(1): 37-88
|
5 |
Embrechts P, Lindskog F, McNeil A. Modelling dependence with copulas and applications to risk management. In: Rachev S, ed. Handbook of Heavy Tailed Distributions in Finance. Amsterdam: Elsevier, 2003
|
6 |
Gordy M. Saddlepoint approximation of credit risk. J Banking Finance2002, 26: 1335-1353
|
7 |
Huang X. Higher-order saddlepoint approximations in the Vasicek portfolio credit loss model. J Comput Finance, 2009, 11(1): 93-113
|
8 |
Huang X, Oosterlee C W. Saddlepoint approximations for expectations. Preprint, 2009
|
9 |
Kaas R, Goovaerts M, Dhaene J, Denuit M. Modern Actuarial Risk Theory. London: Kluwer Academic Publishers, 2001
|
10 |
Lugannani R, Rice S. Saddlepoint approximation for the distribution of the sum of independent random variables. Adv Appl Probab, 1980, 12: 475-490
|
11 |
Martin R, Thompson K, Browne C. Taking to the saddle. In: Gordy M, ed. Credit Risk Modelling: The Cutting-edge Collection. London: Riskbooks, 2003
|
12 |
Reid N. Saddlepoint methods and Statistical Inference. Stat Sci, 1988, 3(2): 213-238
|
13 |
Rogers L C G, Zane O. Saddlepoint approximations to option prices. Ann Appl Probab, 1999, 9(2): 493-503
|
14 |
Studer M. Stochastic Taylor Expansions and Saddlepoint Approximations for Risk Management. <DissertationTip/>. Zürich: ETH Zürich, 2001
|
15 |
Yang Jingping, Hurd Tom, Zhang Xuping. Saddlepoint approximation method for pricing CDOs. J Comput Finance, 2006, 10(1): 1-20
|
/
〈 | 〉 |