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Volumn 26, Issue 5, 2010, Pages 455-489

Dimension-wise integration of high-dimensional functions with applications to finance

Author keywords

ANOVA decomposition; Effective dimension; Numerical integration; Sparse grids

Indexed keywords

ANALYSIS OF VARIANCE (ANOVA);

EID: 78651531432     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2010.06.001     Document Type: Conference Paper
Times cited : (103)

References (41)
  • 2
    • 0026263188 scopus 로고
    • Algorithm 698: DCUHREan adaptive multidimensional integration routine for a vector of integrals
    • J. Bernsten, T. Espelid, and A. Genz Algorithm 698: DCUHREan adaptive multidimensional integration routine for a vector of integrals ACM Trans. Math. Softw. 17 1991 452 456
    • (1991) ACM Trans. Math. Softw. , vol.17 , pp. 452-456
    • Bernsten, J.1    Espelid, T.2    Genz, A.3
  • 4
    • 0003008716 scopus 로고    scopus 로고
    • Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension
    • R. Caflisch, W. Morokoff, and A. Owen Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension J. Comput. Finance 1 1 1997 27 46
    • (1997) J. Comput. Finance , vol.1 , Issue.1 , pp. 27-46
    • Caflisch, R.1    Morokoff, W.2    Owen, A.3
  • 6
    • 85009724776 scopus 로고    scopus 로고
    • Nonlinear approximation
    • R. DeVore Nonlinear approximation Acta Numer. 7 1998 51 150
    • (1998) Acta Numer. , vol.7 , pp. 51-150
    • Devore, R.1
  • 7
    • 0030190203 scopus 로고    scopus 로고
    • Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight
    • A. Genz, and B. Keister Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight J. Comput. Appl. Math. 71 1996 299 309
    • (1996) J. Comput. Appl. Math. , vol.71 , pp. 299-309
    • Genz, A.1    Keister, B.2
  • 8
    • 0242440688 scopus 로고    scopus 로고
    • Numerical integration using sparse grids
    • T. Gerstner, and M. Griebel Numerical integration using sparse grids Numer. Algorithms 18 1998 209 232
    • (1998) Numer. Algorithms , Issue.18 , pp. 209-232
    • Gerstner, T.1    Griebel, M.2
  • 9
    • 0141991028 scopus 로고    scopus 로고
    • Dimension-adaptive tensor-product quadrature
    • T. Gerstner, and M. Griebel Dimension-adaptive tensor-product quadrature Computing 71 1 2003 65 87
    • (2003) Computing , vol.71 , Issue.1 , pp. 65-87
    • Gerstner, T.1    Griebel, M.2
  • 11
    • 49949112371 scopus 로고    scopus 로고
    • Sparse grids and related approximation schemes for higher dimensional problems
    • M. Griebel Sparse grids and related approximation schemes for higher dimensional problems L. Pardo, A. Pinkus, E. Suli, M. Todd, Foundations of Computational Mathematics (FoCM05), Santander 2006 Cambridge University Press 106 161
    • (2006) Foundations of Computational Mathematics (FoCM05), Santander , pp. 106-161
    • Griebel, M.1
  • 12
    • 77956534063 scopus 로고    scopus 로고
    • The smoothing effect of the ANOVA decomposition
    • University of New South Wales
    • M. Griebel, F. Kuo, I. Sloan, The smoothing effect of the ANOVA decomposition, Technical Report, University of New South Wales, 2008.
    • (2008) Technical Report
    • Griebel, M.1    Kuo, F.2    Sloan, I.3
  • 13
    • 18444371457 scopus 로고    scopus 로고
    • Cuba a library for multidimensional numerical integration
    • T. Hahn Cuba a library for multidimensional numerical integration Comput. Phys. Comm. 168 2005 78 95
    • (2005) Comput. Phys. Comm. , vol.168 , pp. 78-95
    • Hahn, T.1
  • 14
    • 2942687314 scopus 로고    scopus 로고
    • Adaptive sparse grids
    • M. Hegland Adaptive sparse grids ANZIAM J. 44 2003 C335 C353
    • (2003) ANZIAM J. , vol.44
    • Hegland, M.1
  • 15
    • 56449086276 scopus 로고    scopus 로고
    • A general dimension reduction technique for derivative pricing
    • J. Imai, and K.S. Tan A general dimension reduction technique for derivative pricing J. Comput. Finance 10 2 2006 129 155
    • (2006) J. Comput. Finance , vol.10 , Issue.2 , pp. 129-155
    • Imai, J.1    Tan, K.S.2
  • 17
    • 0002938637 scopus 로고    scopus 로고
    • Quasi-regression and the relative importance of the ANOVA components of a function
    • C. Lemieux, and A. Owen Quasi-regression and the relative importance of the ANOVA components of a function K.T. Fang, F.J. Hickernell, H. Niederreiter, Monte Carlo and Quasi-Monte Carlo Methods 2000 Springer 331 344
    • (2000) Monte Carlo and Quasi-Monte Carlo Methods , pp. 331-344
    • Lemieux, C.1    Owen, A.2
  • 18
    • 0005737882 scopus 로고    scopus 로고
    • The path integral approach to financial modeling and options pricing
    • V. Linetsky The path integral approach to financial modeling and options pricing Computat. Econ. 11 1998 129 163
    • (1998) Computat. Econ. , vol.11 , pp. 129-163
    • Linetsky, V.1
  • 19
    • 33745668483 scopus 로고    scopus 로고
    • Estimating mean dimensionality of analysis of variance decompositions
    • R. Liu, and A.B. Owen Estimating mean dimensionality of analysis of variance decompositions J. Amer. Statist. Assoc. 101 2006 712 721
    • (2006) J. Amer. Statist. Assoc. , vol.101 , pp. 712-721
    • Liu, R.1    Owen, A.B.2
  • 20
    • 0002622180 scopus 로고    scopus 로고
    • Smoothness and dimension reduction in quasi-Monte Carlo methods
    • B. Moskowitz, and R. Caflisch Smoothness and dimension reduction in quasi-Monte Carlo methods J. Math. Comput. Modeling 23 1996 37 54
    • (1996) J. Math. Comput. Modeling , vol.23 , pp. 37-54
    • Moskowitz, B.1    Caflisch, R.2
  • 21
    • 85013919983 scopus 로고    scopus 로고
    • Toward real-time pricing of complex financial derivatives
    • S. Ninomiya, and S. Tezuka Toward real-time pricing of complex financial derivatives Appl. Math. Finance 3 1996 1 20
    • (1996) Appl. Math. Finance , vol.3 , pp. 1-20
    • Ninomiya, S.1    Tezuka, S.2
  • 22
    • 0030524566 scopus 로고    scopus 로고
    • High dimensional integration of smooth functions over cubes
    • E. Novak, and K. Ritter High dimensional integration of smooth functions over cubes Numer. Math. 75 1996 79 97 (Pubitemid 126343480)
    • (1996) Numerische Mathematik , vol.75 , Issue.1 , pp. 79-97
    • Novak, E.1    Ritter, K.2
  • 24
    • 20144385376 scopus 로고
    • Deterministic simulation for risk management
    • A. Papageorgiou, and S. Paskov Deterministic simulation for risk management J. Portfolio Manag. 25 5 1995 122 127
    • (1995) J. Portfolio Manag. , vol.25 , Issue.5 , pp. 122-127
    • Papageorgiou, A.1    Paskov, S.2
  • 25
    • 0029692966 scopus 로고
    • Faster valuation of financial derivatives
    • S. Paskov, and J. Traub Faster valuation of financial derivatives J. Portfolio Manag. 22 1995 113 120
    • (1995) J. Portfolio Manag. , vol.22 , pp. 113-120
    • Paskov, S.1    Traub, J.2
  • 26
    • 0034421815 scopus 로고    scopus 로고
    • The exponent of discrepancy of sparse grids is at least 2. 1933
    • L. Plaskota The exponent of discrepancy of sparse grids is at least 2. 1933 Adv. Comput. Mat. 12 2000 3 24
    • (2000) Adv. Comput. Mat. , vol.12 , pp. 3-24
    • Plaskota, L.1
  • 27
    • 0035700530 scopus 로고    scopus 로고
    • The exact exponent of sparse grid quadratures in the weighted case
    • L. Plaskota, and G.W. Wasilkowski The exact exponent of sparse grid quadratures in the weighted case J. Complexity 17 2001 840 848
    • (2001) J. Complexity , vol.17 , pp. 840-848
    • Plaskota, L.1    Wasilkowski, G.W.2
  • 28
    • 0033241715 scopus 로고    scopus 로고
    • General foundations of high-dimensional model representations
    • H. Rabitz, and O. Alis General foundations of high-dimensional model representations J. Math. Chem. 25 1999 197 233
    • (1999) J. Math. Chem. , vol.25 , pp. 197-233
    • Rabitz, H.1    Alis, O.2
  • 29
    • 0002522806 scopus 로고    scopus 로고
    • When are quasi-Monte Carlo algorithms efficient for high-dimensional integrals?
    • I. Sloan, and H. Woniakowski When are quasi-Monte Carlo algorithms efficient for high-dimensional integrals? J. Complexity 14 1998 1 33
    • (1998) J. Complexity , vol.14 , pp. 1-33
    • Sloan, I.1    Woniakowski, H.2
  • 30
    • 0038624700 scopus 로고    scopus 로고
    • Constructing randomly shifted lattice rules in weighted Sobolev spaces
    • I.H. Sloan, F.Y. Kuo, and S. Joe Constructing randomly shifted lattice rules in weighted Sobolev spaces SIAM J. Numer. Anal. 40 2002 1650 1665
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 1650-1665
    • Sloan, I.H.1    Kuo, F.Y.2    Joe, S.3
  • 31
    • 0001048297 scopus 로고
    • Quadrature and interpolation formulas for tensor products of certain classes of functions
    • S. Smolyak Quadrature and interpolation formulas for tensor products of certain classes of functions Dokl. Akad. Nauk SSSR 4 1963 240 243
    • (1963) Dokl. Akad. Nauk SSSR , vol.4 , pp. 240-243
    • Smolyak, S.1
  • 32
    • 0000760143 scopus 로고
    • Sensitivity estimates for nonlinear mathematical models
    • I. Sobol Sensitivity estimates for nonlinear mathematical models Math. Mode. and Comput. Exp. 1 1993 407 414
    • (1993) Math. Mode. and Comput. Exp. , vol.1 , pp. 407-414
    • Sobol, I.1
  • 33
    • 0034926426 scopus 로고    scopus 로고
    • Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
    • I. Sobol Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates Math. Comput. Simulation 55 2001 271 280
    • (2001) Math. Comput. Simulation , vol.55 , pp. 271-280
    • Sobol, I.1
  • 34
    • 0037301809 scopus 로고    scopus 로고
    • Theorems and examples on high dimensional model representation
    • I. Sobol Theorems and examples on high dimensional model representation Reliab. Eng. and Syst. Saf. 79 2003 187 193
    • (2003) Reliab. Eng. and Syst. Saf. , vol.79 , pp. 187-193
    • Sobol, I.1
  • 36
    • 33847024936 scopus 로고    scopus 로고
    • On the effects of dimension reduction techniques on some high-dimensional problems in finance
    • X. Wang On the effects of dimension reduction techniques on some high-dimensional problems in finance Oper. Res. 54 6 2006 1063 1078
    • (2006) Oper. Res. , vol.54 , Issue.6 , pp. 1063-1078
    • Wang, X.1
  • 37
    • 60749103359 scopus 로고    scopus 로고
    • On the approximation error in high dimensional model representation
    • in: S. Mason et al. (Eds.)
    • X. Wang, On the approximation error in high dimensional model representation, in: S. Mason et al. (Eds.), Proceeding of the 2008 Winter Simulation Conference, 2008, pp. 453462.
    • (2008) Proceeding of the 2008 Winter Simulation Conference , pp. 453-462
    • Wang, X.1
  • 38
    • 0037389675 scopus 로고    scopus 로고
    • The effective dimension and quasi-Monte Carlo integration
    • X. Wang, and K.-T. Fang The effective dimension and quasi-Monte Carlo integration J. Complexity 19 2 2003 101 124
    • (2003) J. Complexity , vol.19 , Issue.2 , pp. 101-124
    • Wang, X.1    Fang, K.-T.2
  • 39
    • 33144490090 scopus 로고    scopus 로고
    • Why are high-dimensional finance problems often of low effective dimension?
    • X. Wang, and I. Sloan Why are high-dimensional finance problems often of low effective dimension? SIAM J. Sci. Comput. 27 1 2005 159 183
    • (2005) SIAM J. Sci. Comput. , vol.27 , Issue.1 , pp. 159-183
    • Wang, X.1    Sloan, I.2
  • 40
    • 46449084805 scopus 로고
    • Explicit cost bounds of algorithms for multivariate tensor product problems
    • G. Wasilkowski, and H. Woniakowski Explicit cost bounds of algorithms for multivariate tensor product problems J. Complexity 11 1995 1 56
    • (1995) J. Complexity , vol.11 , pp. 1-56
    • Wasilkowski, G.1    Woniakowski, H.2
  • 41
    • 0000212334 scopus 로고    scopus 로고
    • Weighted tensor product algorithms for linear multivariate problems
    • G. Wasilkowski, and H. Woniakowski Weighted tensor product algorithms for linear multivariate problems J. Complexity 15 1999 402 447
    • (1999) J. Complexity , vol.15 , pp. 402-447
    • Wasilkowski, G.1    Woniakowski, H.2


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