WO2001053998A1 - Resource allocation techniques - Google Patents
Resource allocation techniques Download PDFInfo
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- WO2001053998A1 WO2001053998A1 PCT/US2001/000636 US0100636W WO0153998A1 WO 2001053998 A1 WO2001053998 A1 WO 2001053998A1 US 0100636 W US0100636 W US 0100636W WO 0153998 A1 WO0153998 A1 WO 0153998A1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
- G06Q40/08—Insurance
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/15—Correlation function computation including computation of convolution operations
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
- G06Q40/06—Asset management; Financial planning or analysis
Definitions
- the invention concerns techniques for allocating a resource among a number of potential uses for the resource such that a satisfactory tradeoff between a risk and a return on the resource is obtained More particularly, the invention concerns improved techniques for determining the risk-return tradeoff for particular uses, techmques for determining the contribution of uncertainty to the value of the resource, techniques for specifying ⁇ sks, and techniques for quantifying the effects and contiibution of diversification of risks on the risk-return tradeoff and valuation for a given allocation of the resource among the uses
- Resource allocation thus typically involves three steps 1 Selecting a set of uses with different kinds of risks
- the potential value of a resource allocation is not simply what the allocation itself brings, but additionally, the value of being able to undertake future courses of action based on the present resource allocation.
- the value of the license is not just what the license could be sold to a third party for, but the value to the company of the option of being able to enter the new line of business. Even if the company never enters the new line of business, the option is valuable because the option gives the company choices it otherwise would not have had.
- real options and their uses see Keith J. Leslie and Max P. Michaels, "The real power of real options", in: The McKinsey Quarterly, 1997, No. 3, pp. 4-22, and Thomas E. Copland and Philip T. Keenan, "Making real options real", The McKinsey Quarterly, 1998, No. 3, pp. 128-141.
- the resource allocation techniques disclosed herein solve the first of the foregoing problems by providing a technique that uses a real option function in a linear or non-linear optimization program to determine an allocation of investment funds among a set of at least two asset classes for a period of time which will maximize the value of the set of asset classes over the period of time
- the resource allocation techniques solve the second of the foregoing problems by introducing the notion of reliability to quantify the effects of diversification
- the technique determines reliability of a first factor, for example the value of a set of asset classes, which is dependent on a set of at least two second factors, for example asset classes to which the funds have been allocated, where each of the second factors is diversely subject to a third factor, for example uncertainty
- the reliability may be determined by establishing correlations between the second factors with regard to the third factor, using the correlations in determining a standard deviation of the third factor for the set, and using the first factor and the standard deviation in determining the reliability of the first factor with regard to the third factor
- the reliability technique may be used to provide a constraint for linear or non-lmear optimization programs, including ones using the real option function
- the constraint specifies a minimum reliability for the return on the asset classes with regard to the risks associated with the assets Risks involved m
- the reliability restraint may include historic investment risks, political ⁇ sks, or any other kind of quantifiable risk
- FIG. 1 is a flowchart of resource allocation according to the techniques of the invention
- FIG. 2 is a block diagram of a system for allocating investment funds which embodies the techniques of the invention
- FIG. 3 is a block diagram of an implementation of the system of FIG. 3;
- FIG. 4 is a block diagram of a computer system which may be used in the implementation of
- Reference numbers in the drawing have three or more digits: the two right-hand digits are reference numbers in the drawing indicated by the remaining digits. Thus, an item with the reference number 203 first appears as item 203 in FIG. 2.
- Reliability is an important concern for the designers of mechanical, electrical, and electronic systems.
- a system is reliable if it is very likely that it will work correctly.
- Engineers have measured reliability in terms of the probability of failure; the lower the probability of failure, the more reliable the system.
- the probability of failure of a system is determined by analyzing the probability that components of the system will fail in such a way as to cause the system to fail.
- a system's reliability can be increased by providing redundant components.
- An example of the latter technique is the use of triple computers in the space shuttle. All of the computations are performed by each of the computers, with the computers voting to decide which result is correct. If one of the computers repeatedly provides incorrect results, it is shut down by the other two.
- the aspect of resource allocation that performs the same function as redundancy in physical systems is diversification. Part of intelligent allocation of a resource among a number of uses is making sure that the returns for the uses are subject to different risks.
- the resource is land
- the desired return is a minimum amount of corn for livestock feed
- some parts of the land are bottom land that is subject to flooding in wet years
- other parts of the land are upland that is subject to drought in dry years
- the wise farmer will allocate enough of both the bottom land and the upland to corn so that either by itself will yield the minimum amount of corn.
- a wet or dry year there will be the minimum amount of corn, and in a normal year there will be a surplus.
- Reliability analysis can be applied to resource allocation in a manner that is analogous to its application to physical systems.
- the bottom land and the upland are redundant systems in the sense that either is capable by itself of yielding the minimum amount in the wet and dry years respectively, and consequently, the reliability of receiving the minimum amount is very high.
- a given year cannot be both wet and dry, and consequently, there is a low correlation between the risk that the bottom land planting will fail and the risk that the upland planting will fail.
- the less correlation there is between the risks of the various uses for a given return the more reliable the return is.
- FIG. 1 A system that uses real options and reliability to allocate investment funds: FIG. 1
- the resource is investment funds
- the uses for the funds are investments in various classes of assets
- potential valuations of the asset classes resulting from particular allocations of funds are calculated using real options
- the correlations between the risks of the classes of assets are used to determine the reliability of the return for a particular allocation of funds to the asset classes.
- FIG. 1 is a flowchart 101 of the processing done by the system of the preferred embodiment. Processing begins at 103. Next, a set of asset classes is selected (105). Then an expected rate of return and a risk is specified for each asset class (107).
- the source for the expected rate of return for a class and the risk may be based on historical data. In the case of the risk, the historical data may be volatility data. In other embodiments, the expected rate of return may be based on other information and the risk may be any quantifiable uncertainty or combination thereof, including economic risks generally, business risks, political risks or currency exchange rate risks.
- correlations are determined between the risk for the asset class and for every other one of the asset classes (108).
- the purpose of this step is to quantify the diversification of the portfolio.
- the present value of a real option for the asset class for a predetermined time is computed (109).
- an allocation of the funds is found which maximizes the present values of the real options (1 1 1), subject to a reliability constraint which is based on the correlations determined at 108.
- the reliability of a certain average return on the portfolio is found from the average rate of return of the portfolio over a period of time T and the standard deviation ⁇ for the portfolio's return over the period of time T
- the standard deviation for the portfolio represents the volatility of the portfolio's assets over the time T .
- the standard deviation for the portfolio can be found from the standard deviation of each asset over time T and the correlation coefficient p for each pair of asset classes.
- the portfolio standard deviation and the portfolio's rate of return can be written as:
- ⁇ P- ⁇ ' ⁇ ⁇ X Xb AB ⁇ 4,T ⁇ B + ⁇ X ⁇ 2 ⁇ 4
- ⁇ P ⁇ is the standard deviation (or volatility) of the portfolio over T periods of time
- r Pjt is the average rate of return of the portfolio over T periods of time
- X A is the fraction of portfolio invested in asset class A
- P A,B is the correlation of risk for the pair of asset classes A and B; ⁇ A, ⁇ s the standard deviation of asset class A over T periods of time; r A , ⁇ is the average rate of return of asset class A over T periods of time; and
- S is the set of asset classes.
- T A is the time to maturity for an asset class A and x A j is the fraction of the portfolio invested in asset class A during the period of time i, where T A is divided into equal periods 0..T A -1.
- T time to maturity from time period 0 to maturity
- Ex value of the next investment
- r f risk-free rate of interest
- ⁇ volatility
- N A the value of the real option corresponding to the choice of asset class A at time i using the Black-Scholes formula is:
- the above formula is an adaptation of the standard Black-Scholes formula. It differs in two respects: first, it does not assume risk-neutral valuation; second an exponential term has been added to the first term of N A, , and corresponds to the discounted value for a rate of return r a . With these two changes, the real option value is better suited to the context of asset allocation.
- the program being subject to reliability constraints such as the one set forth above.
- FIG. 2 Overview of implementation of the investment funds allocation system: FIG. 2
- Fig. 2 is an overview of an investment funds allocation system 201 that employs the principles of the invention.
- data 203 about the asset classes to which the investment funds are to be allocated
- control variables 207 Included in the data are at least the expected risks and returns for the asset classes and a correlation matrix which correlates the expected risks and expected returns for each of the asset classes with those for each of the other asset classes. The standard deviation for each asset class and the covariance for each pair of asset classes may be computed from this data. Also included in the data may be other risk measures, such as political risk or currency exchange risk. Each risk may have its own correlation matrix or the risks may be combined in a single correlation matrix.
- the control variables 207 include an indication of the minimum return required and an indication of the minimum reliability required.
- the output of system 201 shown at 215, is an allocation of the investment funds to the asset classes. The allocation maximizes the return achieved by the funds for the specified minimum reliability.
- System 201 has two major processing components: reliability model 205, which does the computation of the option values and the reliability constraint needed for the maximization, and reliability engine 21 1, which does the maximization using the option values and the reliability constraint.
- Reliability model 205 computes the reliability constraint from the correlation matrix for the asset classes.
- Reliability engine 213 is controlled by convergence parameters 213.
- One of the parameters is an initial solution for the allocation, which need not be realistic, and another is a convergence precision value, which indicates when successive improvements in the maximizations are so close in value to each other that reliability engine 21 1 may be stopped.
- results from one maximization may be used as a starting point for the next.
- the results of a maximization may be used as an initial solution for the next maximization.
- the convergence precision value may be decreased and/or the minimum reliability may be increased and/or the rate of return increased. If a maximization does not produce a solution, the convergence precision value may be increased and/or the minimum reliability decreased and/or the rate of return decreased.
- feedback mechanism 209 utilizes standard techniques of Automatic Control Theory in order to adjust the convergence precision value and the minimum reliability. Detailed example implementation: FIGs. 3 and 4
- FIG 3 shows an example implementation 301 of system 201
- Example implementation 301 is a prototype implementation that was made using a computer upon which the Microsoft Excel spreadsheet program manufactured by Microsoft Corporation, Redmond, WA, and the Matlab mathematical function program manufactured by The Math Works, Inc , Natick, MA can be executed
- the data used in the system is stored in Excel spreadsheets and the calculations are made by Matlab functions
- the functions read data from and output data to the Excel spreadsheets
- FIG 3 shows the relationship of the components
- the maximization is done by a Matlab minimization function 305 called fmincon (the Matlab function program includes only minimization functions)
- the minimization function takes as arguments an objective function and a constraint function, both user-defined, together with a starting allocation
- the objective function 307 used in the implementation computes the real option value for each of the asset classes
- y ( ⁇ ) -V ( ⁇ ) *x ( ⁇ ) ;
- end f sum (y) x here represents an asset class
- V is a built-in Matlab real option value function v . dat is spreadsheet 311 , which in the prototype contained data on 23 asset classes Since fmincon is a minimization function, the function which is minimized is -V The minimization of -V is of course equivalent to the maximization of V
- the constraint function 309 in the implementation is a function which computes the reliability constraint as described above and applies it along with four other constraints • that there be a positive allocation of each asset class,
- the fragment reads data from spreadsheet 317 and spreadsheet 319 A is thus the cova ⁇ ance matrix and ra the average return for each asset class
- ritiin specifies the minimum return
- beta is the convergence precision value
- n specifies the precision to be used in the computation
- alpha is the minimum reliability
- the remainder of the code fragment computes the value delta, which is used to compute the reliability constraint delta corresponds to ⁇ m the approximation of the reliability restraint Matlab maximization function 305 thus implements reliability engine 21 1
- user-defined objective function 307 and user-defined constraint function 309 implement reliability model
- an asset class data spreadsheet 31 1 contains the data about the asset classes that is required to compute the real option value
- asset class diversification matrix spreadsheet 315 contains correlations between the asset classes and the standard deviation for each asset class, and thus provides the data that is necessary to compute the covariances for the asset classes
- asset class return spreadsheet 319 contains the average return for each of the asset classes.
- the reliability constraint takes only the risk embodied in the volatility of the asset classes over time into account.
- a constraint and convergence parameters file 323 contains parameters 213.
- spreadsheet 31 1 is read by real option objective function 307, which uses the data to compute the real option value for each of the asset classes.
- Asset class diversification matrix spreadsheet 315 is read by reliability constraint function 309, which uses the asset class diversification matrix and the standard deviation to compute a covariance matrix for the asset classes.
- the covariance matrix is output to spreadsheet 317.
- Maximization function 305 uses real option value spreadsheet 313, covariance matrix spreadsheet 317, asset class return spreadsheet 319, and constraint and convergence parameters 323 as inputs in finding the allocation of the investment funds among the asset classes.
- the inputs from covariance matrix spreadsheet 317 and asset class return spreadsheet 319 are used by maximization function 305 to compute the reliability constraint.
- the allocation of the investment funds which obtains the best return subject to the reliability constraint is output to allocation result spreadsheet 321.
- Fig. 4 shows a computer system 401 in which example implementation 301 may be set up and executed.
- System 401 has two main components, storage 403 and processor 41 1.
- Storage 403 may be any storage which is accessible from processor 41 1 , including processor 41 1 's main memory, peripheral storage devices such as disk drives connected to processor 41 1 , and storage which processor 41 1 may access via a network.
- the contents of storage 403 may be distributed in any fashion across the components of storage 403. Logically, the contents of storage 403 may be divided into programs 405, including Excel spreadsheet program 407 and Matlab program 303, and data, which contains the data produced and used by spreadsheet program 407 and Matlab program 303
- Processor 41 1 may be any processor which can execute programs 407 and 303
- the user interface to processor 41 1 is provided by monitor 413, keyboard 415, and mouse 417
- Monitor 413 receives outputs from programs 303 and 407 and a user of implementation 301 provides inputs to these programs using keyboard 415 and/or mouse 417
- the components of FIG 4 may be further distributed in various fashions across a network At one extreme, all may be part of a single processor system, at another, part of processor 41 1 may function functioning as a Web browser that provides output to and receives input from monitor 413, keyboard 415, and mouse 417 and all of the other components may be accessible to the browser part of processor 41 1 via the Internet
- other parts of processor 41 1 may be located m a Web server and the storage 403 may be located anywhere that is accessible to the server
- the embodiment just described employs a reliability constraint that is derived from the past volatility of each asset class
- reliability constraints based on other risks may be easily added to the list
- the only requirement is that the restraint be quantifiable on a per-asset class basis
- Political risk provides an example here at page 100 of the June 22, 1996 Economist may be found national credit-risk ratings for a number of countries
- the "quantification" may simply be a matter of an expert giving a value for a particular risk to each of the asset classes
- Risks may also be combined within a single reliability constraint, for example, by allocating a portion of the total reliability constraint to each risk
- Reliability constraints like the ones just described for the rate of return on a portfolio of investments may be used for any attribute of a set of entities whose value is aggregated from attributes of the entities which are subject to a variation which can be described in terms of a standard deviation for the individual entity and correlation matrices for combinations of the entities
- the constraint may be used with any kind of computation where it makes sense, and it may be used to select among possible outputs of a computation, as in the embodiments described herein, or it may be used to select among possible inputs to a computation
- An example of a general-purpose problem-solving system m which reliability constraints could be usefully employed is the one disclosed in U S Patent 5,428,712, Elad, et al , System and method for i epresenting and solving numeric and symbolic problems issued 27 June 1995
- the combination of real options with reliability constraints can be used with many applications of real options For applications of real options, see the Copeland and Keenan reference mentioned above
Abstract
Description
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Priority Applications (6)
Application Number | Priority Date | Filing Date | Title |
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BR0107495-4A BR0107495A (en) | 2000-01-10 | 2001-01-09 | Resource Allocation Techniques |
JP2001554224A JP2003521043A (en) | 2000-01-10 | 2001-01-09 | Resource allocation technology |
IL15062701A IL150627A0 (en) | 2000-01-10 | 2001-01-09 | Resource allocation techniques |
EP01942749A EP1248997A4 (en) | 2000-01-10 | 2001-01-09 | Resource allocation techniques |
CA002394315A CA2394315A1 (en) | 2000-01-10 | 2001-01-09 | Resource allocation techniques |
KR1020027008914A KR20020079777A (en) | 2000-01-10 | 2001-01-09 | Resource allocation techniques |
Applications Claiming Priority (2)
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US17526100P | 2000-01-10 | 2000-01-10 | |
US60/175,261 | 2000-01-10 |
Publications (1)
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WO2001053998A1 true WO2001053998A1 (en) | 2001-07-26 |
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PCT/US2001/000636 WO2001053998A1 (en) | 2000-01-10 | 2001-01-09 | Resource allocation techniques |
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EP (1) | EP1248997A4 (en) |
JP (1) | JP2003521043A (en) |
KR (2) | KR20070120199A (en) |
CN (1) | CN1395706A (en) |
BR (1) | BR0107495A (en) |
CA (1) | CA2394315A1 (en) |
IL (1) | IL150627A0 (en) |
MA (1) | MA27345A1 (en) |
TW (1) | TW493130B (en) |
WO (1) | WO2001053998A1 (en) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
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JP2007526533A (en) * | 2003-06-04 | 2007-09-13 | プロフィトロジック インコーポレイテッド | Method and apparatus for retail inventory budget optimization and gross profit maximization |
Families Citing this family (2)
Publication number | Priority date | Publication date | Assignee | Title |
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JP2007265295A (en) * | 2006-03-29 | 2007-10-11 | Fujitsu Ltd | Customer support system |
US7958038B2 (en) * | 2006-06-22 | 2011-06-07 | Yves Choueifaty | Methods and systems for providing an anti-benchmark portfolio |
Citations (4)
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US5784696A (en) * | 1995-02-24 | 1998-07-21 | Melnikoff; Meyer | Methods and apparatus for evaluating portfolios based on investment risk |
US5812987A (en) * | 1993-08-18 | 1998-09-22 | Barclays Global Investors, National Association | Investment fund management method and system with dynamic risk adjusted allocation of assets |
US5812988A (en) * | 1993-12-06 | 1998-09-22 | Investments Analytic, Inc. | Method and system for jointly estimating cash flows, simulated returns, risk measures and present values for a plurality of assets |
US5884287A (en) * | 1996-04-12 | 1999-03-16 | Lfg, Inc. | System and method for generating and displaying risk and return in an investment portfolio |
Family Cites Families (3)
Publication number | Priority date | Publication date | Assignee | Title |
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JPH1196218A (en) * | 1997-09-16 | 1999-04-09 | Mit:Kk | Automatic port folio designing system and storage medium |
JPH11110447A (en) * | 1997-10-06 | 1999-04-23 | Pfps Kenkyukai:Kk | Total portfolio planning system |
US6003018A (en) * | 1998-03-27 | 1999-12-14 | Michaud Partners Llp | Portfolio optimization by means of resampled efficient frontiers |
-
2001
- 2001-01-09 WO PCT/US2001/000636 patent/WO2001053998A1/en not_active Application Discontinuation
- 2001-01-09 BR BR0107495-4A patent/BR0107495A/en not_active IP Right Cessation
- 2001-01-09 IL IL15062701A patent/IL150627A0/en unknown
- 2001-01-09 CA CA002394315A patent/CA2394315A1/en not_active Abandoned
- 2001-01-09 KR KR1020077027205A patent/KR20070120199A/en not_active Application Discontinuation
- 2001-01-09 EP EP01942749A patent/EP1248997A4/en not_active Withdrawn
- 2001-01-09 CN CN01803596A patent/CN1395706A/en active Pending
- 2001-01-09 KR KR1020027008914A patent/KR20020079777A/en not_active Application Discontinuation
- 2001-01-09 JP JP2001554224A patent/JP2003521043A/en active Pending
- 2001-03-09 TW TW090100515A patent/TW493130B/en not_active IP Right Cessation
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2002
- 2002-06-28 MA MA26716A patent/MA27345A1/en unknown
Patent Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
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US5812987A (en) * | 1993-08-18 | 1998-09-22 | Barclays Global Investors, National Association | Investment fund management method and system with dynamic risk adjusted allocation of assets |
US5812988A (en) * | 1993-12-06 | 1998-09-22 | Investments Analytic, Inc. | Method and system for jointly estimating cash flows, simulated returns, risk measures and present values for a plurality of assets |
US5784696A (en) * | 1995-02-24 | 1998-07-21 | Melnikoff; Meyer | Methods and apparatus for evaluating portfolios based on investment risk |
US5884287A (en) * | 1996-04-12 | 1999-03-16 | Lfg, Inc. | System and method for generating and displaying risk and return in an investment portfolio |
Non-Patent Citations (1)
Title |
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See also references of EP1248997A4 * |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2007526533A (en) * | 2003-06-04 | 2007-09-13 | プロフィトロジック インコーポレイテッド | Method and apparatus for retail inventory budget optimization and gross profit maximization |
Also Published As
Publication number | Publication date |
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EP1248997A1 (en) | 2002-10-16 |
MA27345A1 (en) | 2005-06-01 |
EP1248997A4 (en) | 2005-09-07 |
JP2003521043A (en) | 2003-07-08 |
IL150627A0 (en) | 2003-02-12 |
BR0107495A (en) | 2003-01-14 |
KR20070120199A (en) | 2007-12-21 |
CN1395706A (en) | 2003-02-05 |
TW493130B (en) | 2002-07-01 |
KR20020079777A (en) | 2002-10-19 |
CA2394315A1 (en) | 2001-07-26 |
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