 |
|
|
|
|
|
 Title: |
US5940810:
Estimation method and system for complex securities using low-discrepancy deterministic sequences
[ Derwent Title ]
|
| Country: |
US United States of America
|
| |
| Inventor: |
Traub, Joseph F.; New York, NY
Paskov, Spassimir; New York, NY
Vanderhoof, Irwin F.; Towaco, NJ
|
| Assignee: |
The Trustees of Columbia University in the City of New York, New York, NY
other patents from COLUMBIA UNIVERSITY (112155) (approx. 555)
News, Profiles, Stocks and More about this company
|
| Published / Filed: |
1999-08-17
/ 1997-07-30
|
| Application Number: |
US1997000902921
|
| IPC Code: |
Advanced:
G06Q 40/00;
Core:
more...
IPC-7:
G06F 17/60;
|
| ECLA Code: |
G06Q40/00D;
|
| U.S. Class: |
Current:
705/036.R;
705/037;
Original:
705/036;
705/037;
|
| Field of Search: |
705/035,36,37,8
|
| Government Interest: |
SPECIFICATION
The United States Government has certain rights to this invention pursuant to grants CCR-91-14042 and IRI-92-12597 awarded by the National Science Foundation, and to grant AFOSR-91-0347 awarded by the U.S. Air Force.
|
| Priority Number: |
|
| Abstract: |
In securities trading, in setting the initial offering price of a financial instrument, or in later revaluation as financial parameters such as interest rates may change, an estimate of the value of the instrument may be represented as a multi-dimensional integral. For evaluation of the integral, numerical integration is preferred with the integrand being sampled at deterministic points having a low-discrepancy property. The technique produces approximate values at significant computational savings and with greater reliability as compared with the Monte Carlo technique.
|
| Attorney, Agent or Firm: |
Baker & Botts, L.L.P. ;
|
| Primary / Asst. Examiners: |
Weinhardt, Robert A.;
|
| Maintenance Status: |
CC Certificate of Correction issued
|
| INPADOC Legal Status: |
Show legal status actions
Family Legal Status Report
|
|
|
|
|
|
|
| Parent Case: |
This application is a continuation of application Ser. No. 08/285,902, filed on Aug. 4, 1994, now abandoned.
|
| Family: |
Show 6 known family members
|
First Claim:
Show all 22 claims |
We claim:
1. A method for one of buying, holding and selling a complex security, comprising:
- (i) deriving a multivariate integrand which, when integrated over a domain of integration having at least 50 dimensions, represents an estimated value of the security;
- (ii) calculating, by computer, integrand values at points in the domain of integration which are obtained from a low-discrepancy deterministic sequence;
- (iii) combining the integrand values, by computer, to approximate the estimated value; and
- (iv) effecting, based on the estimated value, one of buying, holding and selling the security.
|
| Background / Summary: |
Show background / summary
|
| Drawing Descriptions: |
Show drawing descriptions
|
| Description: |
Show description
|
| Forward References: |
Show 49 U.S. patent(s) that reference this one
|
|
|
|
|
|
|
| Foreign References: |
None
|
| Other Abstract Info: |
DERABS G1999-468566
DERABS G1999-468566
DERABS G2000-375065
|
| Other References: |
Niederreiter, H., "Random Number Generation and Quasi-Monte Carlo Methods", CBMS-NSF, 63, Siam, Philadelphia 1992, pp. 1-45.
M. Karlos et al., "Monte Carlo Methods", John Wiley & Sons, 1986 pp. 89-117.
H. Wozniakowski, "Average Case Complexity of Linear Multivariate Problems", Journal of Complexity 8 pp. 373-392, 1992.
H. Wozniakowski, "Average Case Complexity of Multivariate Integration", Bulletin of Amer. Math. Society, vol. 24, No. 1, Jan. 1991, pp. 185-194.
(10 pages)
[ISI abstract]
B.W. Kernighan et al., The Programming Language C, Prentice-Hall, 1978, Cover Page and Table of Contents only.
H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF, 63, SIAM, Philadelphia, 1992. Cover Page and Table of Contents only.
S. Paskov, "Average Case Complexity of Multivariate Integration for Smooth Functions", Journal of Complexity, vol. 9 (1993), pp. 291-312.
W. Press et al., Numerical Recipes in C, Cambridge University Press, 1992, Cover page and Table of Contents only.
M. Kalos et al., Monte Carlo Methods, John Wiley & Sons, 1986, Cover Page, Preface and Table of Contents only.
P. Bratley, B. L. Fox and H. Niederreiter, "Implementation and Tests of Low-Discrepancy Sequences", ACM Transactions on Modeling and Computer Simulation, vol. 2 (1992), pp. 195-213.
E. J. Janse van Rensburg et al., "Estimation of Multidimensional Integrals: Is Monte Carlo the Best Method?", J. Phys. A: Math. Gen., vol. 26 (1993), pp. 943-953.
(11 pages)
[ISI abstract]
I.M. Sobol, A Primer for the Monte Carlo Method, CRC Press, 1994, pp. 99, 104.
B. Moskowitz et al., "Smoothness and Dimension Reduction in Quasi-Monte Carlo Methods", Mathematical and Computational Modelling, vol. 23 (1996), pp. 37-54.
(18 pages)
[ISI abstract]
S. Tezuka, Uniform Random Numbers: Theory and Practice, Kluwer Academic Publishers, 1995, pp. xi-xii.
S. Tezuka, "A Generalization of Faure Sequences and its Efficient Implementation", IBM Research Report RT0105, Nov. 14, 1994, pp. 1, 5, 6, 10.
S. Ninomiya and S. Tezuka, "Toward Real-time Pricing of Complex Financial Derivatives", Applied Mathematical Finance, vol. 3 (1996), pp. 1, 2, 20.
S.H. Paskov, "Computing High-dimensional Integrals with Applications to Finance", Columbia University Technical Report CUCS-023-94, pp. 1-20.
J. Case, "Wall Street's Dalliance with Number Theory", SIAM News, Dec. 1995, pp. 8-9.
B. Cipra, What's Happening in the Mathematical Sciences (1995-1996), vol. 3, American Mathematical Society, 1996, pp. 101-111.
|
|
 Nominate this for the Gallery...
|
|
