WO2020000718A1 - Procédé et appareil de génération de portefeuille d'investissement, et support d'information lisible par ordinateur - Google Patents

Procédé et appareil de génération de portefeuille d'investissement, et support d'information lisible par ordinateur Download PDF

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WO2020000718A1
WO2020000718A1 PCT/CN2018/107502 CN2018107502W WO2020000718A1 WO 2020000718 A1 WO2020000718 A1 WO 2020000718A1 CN 2018107502 W CN2018107502 W CN 2018107502W WO 2020000718 A1 WO2020000718 A1 WO 2020000718A1
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matrix
sample
transaction data
target market
market index
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PCT/CN2018/107502
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Chinese (zh)
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李海疆
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平安科技（深圳）有限公司
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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
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0635—Risk analysis of enterprise or organisation activities
    • 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
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • 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
    • G06Q40/04—Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange

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  • the present application relates to the field of information processing technology, and in particular, to a method, a device, and a computer-readable storage medium for generating a portfolio.
  • This application provides a method, device, and computer-readable storage medium for generating a portfolio, the main purpose of which is to implement denoising processing on the sample covariance matrix and reduce the risk of the portfolio.
  • this application also provides a method for generating a portfolio, which method includes:
  • the present application further provides an investment portfolio generation device, which includes a memory and a processor, where the memory stores an investment portfolio generation program that can be run on the processor, and the investment portfolio When the generated program is executed by the processor, the following steps are implemented:
  • the present application further provides a computer-readable storage medium, where the computer-readable storage medium stores a portfolio generation program, and the portfolio generation program can be executed by one or more processors. To achieve the following steps:
  • the investment portfolio generation method, device and computer-readable storage medium proposed in this application determine the target market index, and generate a sample matrix based on the transaction data of the constituent stocks of the target market index over multiple consecutive historical trading days; calculate the target based on the sample matrix
  • the first sample covariance matrix of the constituent stocks of the market index calculates the eigenvalues of the first sample covariance matrix and the eigenvectors corresponding to the eigenvalues; calculates the theoretical maximum eigenvalue of the first sample covariance matrix based on MP's law , Performing a denoising process on the eigenvalues of the first sample covariance matrix based on the eigenvalues and the theoretical maximum eigenvalues; calculating the second based on the eigenvalues diagonal matrix and the matrix composed of eigenvectors after denoising Sample covariance matrix; calculate the investment proportion of each constituent stock based on the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio based on the investment proportion.
  • This solution is based on MP's law to denoise the sample covariance matrix of the market index and filter out the random data, so that the data in the recalculated second sample covariance matrix is a relatively reliable correlation coefficient, which makes investment
  • the portfolio is optimized to reduce investment risks.
  • FIG. 1 is a schematic flowchart of an investment portfolio generation method according to an embodiment of the present application
  • FIG. 2 is a schematic diagram of an internal structure of an investment portfolio generating device according to an embodiment of the present application
  • FIG. 3 is a schematic diagram of a module of a portfolio generation program in a portfolio generation device provided by an embodiment of the present application.
  • This application provides a method for generating a portfolio.
  • a schematic flowchart of a method for generating a portfolio provided by an embodiment of the present application is shown. The method may be performed by a device, which may be implemented by software and / or hardware.
  • the method for generating a portfolio includes:
  • step S10 a target market index is determined, and a sample matrix is generated according to the transaction data of the constituent stocks of the target market index over multiple consecutive historical trading days.
  • Step S20 Calculate a first sample covariance matrix of the constituent stocks of the target market index according to the sample matrix.
  • the target market index in this application may be a market index such as the Shanghai Composite Index, Shanghai and Shenzhen 300.
  • the method of this application will be described using the Shanghai and Shenzhen 300 as an example.
  • step S10 includes the following detailed steps:
  • the target market index is determined, and transaction data of constituent stocks of the target market index within multiple consecutive historical trading days is obtained; the acquired transaction data is standardized; and the sample matrix is constructed according to the standardized processed transaction data.
  • the closing price data is used as financial time series data, it has the characteristics of peaks and fat tails.
  • the log closing data of the stock is first processed:
  • the logarithmic rate of return is standardized.
  • the standardized treatment method is as follows:
  • T is the total number of trading days
  • ⁇ i is the standard deviation of the logarithmic yield of stock i.
  • the number of component bonds in the target market index is N.
  • N 300
  • T 300
  • All the logarithmic return data after normalization process form a N ⁇ T matrix.
  • the logarithmic yield of a constituent stock can be regarded as a random variable, and the logarithmic yield of all constituent stocks in T trading days constitutes a sample logarithmic yield matrix.
  • the logarithmic return sequence matrix of all constituent stocks after normalization is as follows:
  • the first sample covariance matrix obtained is an N ⁇ N matrix.
  • Step S30 Calculate a feature value of the first sample covariance matrix and a feature vector corresponding to the feature value.
  • Step S40 Calculate the theoretical maximum eigenvalue of the first sample covariance matrix based on the M-P law, and perform denoising processing on the angular matrix of the eigenvalues of the first sample covariance matrix based on the theoretical maximum eigenvalue.
  • Step S50 Calculate a second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix composed of the eigenvectors after the denoising process.
  • Step S60 Calculate the investment ratio of each constituent stock according to the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio according to the investment ratio.
  • Step S40 may include the following detailed steps: calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on MP law; arranging the eigenvalues in ascending order to generate a diagonal matrix of eigenvalues; from The eigenvalues of the first sample covariance matrix that are greater than the theoretical maximum eigenvalue and whose previous eigenvalue is less than the theoretical maximum eigenvalue are found as the intercept point eigenvalues; the eigenvalue pairs are deleted Eigenvalues in the angular matrix that are smaller than the eigenvalues of the intercept points are used to denoise the angular matrix on the characteristic values.
  • the eigenvalues ⁇ (i) of the first sample covariance matrix are solved, and the eigenvalues are sorted in ascending order of the eigenvalues ⁇ (1) ⁇ (2) ⁇ ... ⁇ (N) .
  • the values form the eigenvalue diagonal matrix ⁇ :
  • u (i) is a feature vector corresponding to ⁇ (i)
  • the feature vector is a column vector
  • the intercept point eigenvalues are found. Specifically, the eigenvalues ⁇ (1) , ⁇ (2) , ... are arranged in ascending order. In ⁇ (N) , the k-th largest eigenvalue ⁇ (k) is found so that it meets the following conditions:
  • ⁇ (k-1) is the eigenvalue ranked one ahead of ⁇ (k) .
  • ⁇ (k) be the eigenvalue of the intercept point, and replace all eigenvalues whose eigenvalues in the eigenvalue diagonal matrix are smaller than the eigenvalue of the intercept point with 0.
  • the theoretical maximum eigenvalues are consistent with If the eigenvalues calculated based on actual data are greater than the theoretical maximum eigenvalues, it means that some elements in the matrix are not independent and identically distributed, but have a certain correlation.
  • the eigenvalues that conform to MP's law are deleted, and the second covariance matrix recalculated from the diagonal matrix based on the new eigenvalues excludes random data, and the remaining data is relatively reliable related data.
  • the theoretical minimum eigenvalue of the first sample covariance matrix can also be calculated according to MP's law, and for eigenvalues smaller than the theoretical characteristic minimum, the absolute value is generally close to 0 and can be ignored Neglect, and the smaller the eigenvalue, the lower its importance, which can be ignored. Therefore, in the solution of this embodiment, all the eigenvalues smaller than the theoretical maximum eigenvalue are deleted from the diagonal matrix of eigenvalues.
  • the eigenvalues also include those that do not conform to MP's law and are smaller than the theoretical minimum eigenvalue.
  • step S40 may include the following thinning steps: calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on MP law; arranging the eigenvalues in ascending order, Generate a eigenvalue diagonal array; delete the eigenvalues from the eigenvalue diagonal array that are smaller than the theoretical maximum eigenvalue to perform denoising processing on the eigenvalue diagonal array.
  • the covariance matrix is recalculated according to the eigenvalue decomposition formula to obtain the second sample covariance matrix, which has eliminated the influence of the white noise data:
  • U is a matrix composed of the feature vector
  • U -1 is an inverse matrix of the matrix composed of the feature vector
  • ⁇ filtered is a diagonal matrix of eigenvalues after denoising processing.
  • the denoised sample covariance matrix is substituted into the Markowitz mean variance model, the investment proportion of each constituent stock is solved, and the constituent stocks are combined according to the calculated investment proportion to generate an investment portfolio.
  • the sample covariance matrix after denoising is used to calculate in the Markowitz mean variance model, so that the calculated portfolio is optimized and the risk of the portfolio is reduced.
  • the investment portfolio generation method proposed in this embodiment determines the target market index, and generates a sample matrix based on the transaction data of the constituent stocks of the target market index over multiple consecutive historical trading days; and calculates the first component constituents of the target market index based on the sample matrix.
  • a sample covariance matrix calculate the eigenvalues of the first sample covariance matrix and the eigenvectors corresponding to the eigenvalues; calculate the theoretical maximum eigenvalue of the first sample covariance matrix based on MP's law, according to the eigenvalues and the theoretical maximum
  • the eigenvalues denoise the diagonal matrix of the eigenvalues of the first sample covariance matrix; calculate the second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix composed of the eigenvectors after denoising;
  • the two-sample covariance matrix and the Markowitz mean variance model calculate the investment proportion of each constituent stock, and generate an investment portfolio based on the investment proportion.
  • This solution is based on MP's law to denoise the sample covariance matrix of the market index and filter out the random data, so that the data in the recalculated second sample covariance matrix is a relatively reliable correlation coefficient, which makes investment
  • the portfolio is optimized to reduce investment risks.
  • the present application also provides an investment portfolio generation device.
  • FIG. 2 a schematic diagram of an internal structure of an investment portfolio generation device according to an embodiment of the present application is shown.
  • the investment portfolio generation device 1 may be a PC (Personal Computer) or a terminal device such as a smart phone, a tablet computer, or a portable computer.
  • the portfolio generating device 1 includes at least a memory 11, a processor 12, a network interface 13, and a communication bus.
  • the memory 11 includes at least one type of readable storage medium.
  • the readable storage medium includes a flash memory, a hard disk, a multimedia card, a card-type memory (for example, SD or DX memory, etc.), a magnetic memory, a magnetic disk, an optical disk, and the like.
  • the memory 11 may be an internal storage unit of the portfolio generation device 1 in some embodiments, such as a hard disk of the portfolio generation device 1.
  • the memory 11 may also be an external storage device of the portfolio generation device 1 in other embodiments, for example, a plug-in hard disk, a Smart Media Card (SMC), and a secure digital (Secure) Digital, SD) card, Flash card, etc.
  • the memory 11 may further include both an internal storage unit of the portfolio generation device 1 and an external storage device.
  • the memory 11 can be used not only to store application software installed in the portfolio generation device 1 and various types of data, such as the code of the portfolio generation program 01, but also to temporarily store data that has been or will be output.
  • the processor 12 may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip in some embodiments, and is configured to run program codes or processes stored in the memory 11 Data, such as execution of portfolio creation program 01.
  • CPU central processing unit
  • controller controller
  • microcontroller microcontroller
  • microprocessor or other data processing chip in some embodiments, and is configured to run program codes or processes stored in the memory 11 Data, such as execution of portfolio creation program 01.
  • the network interface 13 may optionally include a standard wired interface, a wireless interface (such as a WI-FI interface), and is generally used to establish a communication connection between the device 1 and other electronic devices.
  • a standard wired interface such as a WI-FI interface
  • the communication bus is used to implement connection communication between these components.
  • the device 1 may further include a user interface.
  • the user interface may include a display, an input unit such as a keyboard, and the optional user interface may further include a standard wired interface and a wireless interface.
  • the display may be an LED display, a liquid crystal display, a touch-type liquid crystal display, an OLED (Organic Light-Emitting Diode, organic light emitting diode) touch device, or the like.
  • the display may also be appropriately referred to as a display screen or a display unit for displaying information processed in the portfolio generating device 1 and a user interface for displaying visualization.
  • FIG. 2 only shows a portfolio generation device 1 having components 11-13 and a portfolio generation program 01.
  • FIG. 1 does not constitute a limitation on the portfolio generation device 1 , Can include fewer or more components than shown, or combine certain components, or different component arrangements.
  • the investment portfolio generation program 01 is stored in the memory 11; when the processor 12 executes the investment portfolio generation program 01 stored in the memory 11, the following steps are implemented:
  • the target market index is determined, and a sample matrix is generated based on the transaction data of the constituent stocks of the target market index over consecutive consecutive historical trading days.
  • a first sample covariance matrix of the constituent stocks of the target market index is calculated according to the sample matrix.
  • the theoretical maximum eigenvalue of the first sample covariance matrix is calculated based on the M-P law, and the eigenvalues of the first sample covariance matrix are denoised to the angular matrix according to the theoretical maximum eigenvalue.
  • the target market index in this application may be a market index such as the Shanghai Composite Index, Shanghai and Shenzhen 300.
  • the method of this application will be described using the Shanghai and Shenzhen 300 as an example.
  • the step of determining a target market index, and generating a sample matrix based on the transaction data of the constituent stocks of the target market index over multiple consecutive historical trading days specifically includes the following detailed steps: determining the target market index, and obtaining the target The transaction data of the constituent stocks of the market index within a plurality of consecutive historical trading days; the acquired transaction data is standardized; and the sample matrix is constructed according to the standardized processed transaction data.
  • the closing price data is used as financial time series data, it has the characteristics of peaks and fat tails.
  • the log closing data of the stock is first processed:
  • the logarithmic rate of return is standardized.
  • the standardized treatment method is as follows:
  • T is the total number of trading days
  • ⁇ i is the standard deviation of the logarithmic yield of stock i.
  • the number of component bonds in the target market index is N.
  • N 300
  • T 300
  • All the logarithmic return data after normalization process form a N ⁇ T matrix.
  • the logarithmic yield of a constituent stock can be regarded as a random variable, and the logarithmic yield of all constituent stocks in T trading days constitutes a sample logarithmic yield matrix.
  • the logarithmic return sequence matrix of all constituent stocks after normalization is as follows:
  • the first sample covariance matrix obtained is an N ⁇ N matrix.
  • Calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on the MP law, and performing a step of denoising the angular matrix on the eigenvalues of the first sample covariance matrix according to the theoretical maximum eigenvalue may include: The detailed steps are as follows: the theoretical maximum eigenvalue of the first sample covariance matrix is calculated based on MP law; the eigenvalues are arranged in order from small to large to generate a diagonal matrix of eigenvalues; from the first sample The eigenvalues of the covariance matrix that are greater than the theoretical maximum eigenvalue and whose previous eigenvalue is less than the theoretical maximum eigenvalue are found as the intercept point eigenvalues; delete the eigenvalues that are less than A feature value of the intercept point feature value to perform a denoising process on the feature matrix to the angular matrix.
  • the eigenvalues ⁇ (i) of the first sample covariance matrix are solved, and the eigenvalues are sorted in ascending order of the eigenvalues ⁇ (1) ⁇ (2) ⁇ ... ⁇ (N) .
  • the values form the eigenvalue diagonal matrix ⁇ :
  • u (i) is a feature vector corresponding to ⁇ (i)
  • the feature vector is a column vector
  • the intercept point eigenvalues are found. Specifically, the eigenvalues ⁇ (1) , ⁇ (2) , ... are arranged in ascending order. In ⁇ (N) , the k-th largest eigenvalue ⁇ (k) is found so that it meets the following conditions:
  • ⁇ (k-1) is the eigenvalue ranked one ahead of ⁇ (k) .
  • ⁇ (k) be the eigenvalue of the intercept point, and replace all eigenvalues whose eigenvalues in the eigenvalue diagonal matrix are smaller than the eigenvalue of the intercept point with 0.
  • the theoretical maximum eigenvalues are consistent with If the eigenvalues calculated based on actual data are greater than the theoretical maximum eigenvalues, it means that some elements in the matrix are not independent and identically distributed, but have a certain correlation.
  • the eigenvalues that conform to MP's law are deleted, and the second covariance matrix recalculated from the diagonal matrix based on the new eigenvalues excludes random data. The remaining data is relatively reliable related data.
  • the theoretical minimum eigenvalue of the first sample covariance matrix can also be calculated according to MP's law, and for eigenvalues smaller than the theoretical characteristic minimum, the absolute value is generally close to 0 and can be ignored Neglect, and the smaller the eigenvalue, the lower its importance, which can be ignored. Therefore, in the solution of this embodiment, all the eigenvalues smaller than the theoretical maximum eigenvalue are deleted from the diagonal matrix of eigenvalues.
  • the eigenvalues also include those that do not conform to MP's law and are smaller than the theoretical minimum eigenvalue.
  • a theoretical maximum eigenvalue of the first sample covariance matrix is calculated based on MP law, and a diagonal matrix of eigenvalues of the first sample covariance matrix is calculated based on the theoretical maximum eigenvalue.
  • the step of performing the denoising processing may include the following thinning steps: calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on MP law; arranging the eigenvalues in order from small to large to generate eigenvalue pairs An angular matrix; deleting the eigenvalues of the eigenvalue diagonal matrix that are smaller than the theoretical maximum eigenvalue to perform a denoising process on the eigenvalues of the angular matrix.
  • the covariance matrix is recalculated according to the eigenvalue decomposition formula to obtain the second sample covariance matrix, which has eliminated the influence of the white noise data:
  • U is a matrix composed of the feature vector
  • U -1 is an inverse matrix of the matrix composed of the feature vector
  • ⁇ filtered is a diagonal matrix of eigenvalues after denoising processing.
  • the denoised sample covariance matrix is substituted into the Markowitz mean variance model, the investment proportion of each constituent stock is solved, and the constituent stocks are combined according to the calculated investment proportion to generate an investment portfolio.
  • the sample covariance matrix after denoising is used to calculate in the Markowitz mean variance model, so that the calculated portfolio is optimized and the risk of the portfolio is reduced.
  • the investment portfolio generation device proposed in this embodiment determines a target market index, and generates a sample matrix based on the transaction data of the component stocks of the target market index over multiple consecutive historical trading days; and calculates the first component constituents of the target market index based on the sample matrix.
  • a sample covariance matrix calculate the eigenvalues of the first sample covariance matrix and the eigenvectors corresponding to the eigenvalues; calculate the theoretical maximum eigenvalue of the first sample covariance matrix based on MP's law, according to the eigenvalues and the theoretical maximum
  • the eigenvalues denoise the diagonal matrix of the eigenvalues of the first sample covariance matrix; calculate the second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix composed of the eigenvectors after denoising;
  • the two-sample covariance matrix and the Markowitz mean variance model calculate the investment proportion of each constituent stock, and generate an investment portfolio based on the investment proportion.
  • This solution is based on MP's law to denoise the sample covariance matrix of the market index and filter out the random data, so that the data in the recalculated second sample covariance matrix is a relatively reliable correlation coefficient, which makes investment
  • the portfolio is optimized to reduce investment risks.
  • the investment portfolio generation program may also be divided into one or more modules, and the one or more modules are stored in the memory 11 and implemented by one or more processors (this embodiment It is executed by the processor 12) to complete the present application.
  • the module referred to in the present application refers to a series of computer program instruction segments capable of performing specific functions, and is used to describe the execution process of the investment portfolio generation program in the investment portfolio generation device.
  • FIG. 3 a schematic diagram of a program module of a portfolio generation program in an embodiment of the portfolio generation device of the present application.
  • the portfolio generation program can be divided into a sample generation module 10 and a covariance calculation.
  • the module 20, the feature calculation module 30, the matrix denoising module 40, and the combination generation module 50 for example:
  • the sample generation module 10 is configured to determine a target market index, and generate a sample matrix according to the transaction data of the constituent stocks of the target market index over multiple consecutive historical trading days;
  • the covariance calculation module 20 is configured to calculate a first sample covariance matrix of the constituent stocks of the target market index according to the sample matrix;
  • the feature calculation module 30 is configured to calculate a feature value of the first sample covariance matrix and a feature vector corresponding to the feature value;
  • the matrix denoising module 40 is configured to calculate a theoretical maximum eigenvalue of the first sample covariance matrix based on the MP law, and diagonally compare the eigenvalues of the first sample covariance matrix based on the theoretical maximum eigenvalue. Denoising
  • the covariance calculation module 20 is further configured to calculate a second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix formed by the feature vector after the denoising process;
  • the combination generation module 50 is configured to calculate an investment ratio of each component stock according to the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio according to the investment ratio.
  • an embodiment of the present application further provides a computer-readable storage medium, where the computer-readable storage medium stores a portfolio generation program, and the portfolio generation program can be executed by one or more processors to achieve the following: operating:

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Abstract

L'invention concerne un procédé et un appareil de génération de portefeuille d'investissement, et un support d'information lisible par ordinateur. Le procédé consiste à : générer une matrice d'échantillon en fonction de données de transaction d'actions constitutives d'un indice de marché cible dans une pluralité de jours de négociation historiques consécutifs (S10); calculer une première matrice de covariance d'échantillon en fonction de la matrice d'échantillon (S20); calculer une valeur propre de la première matrice de covariance d'échantillon et un vecteur propre correspondant à la valeur propre (S30); calculer la valeur propre maximale théorique de la première matrice de covariance d'échantillon sur la base de la loi M-P, et débruiter une matrice diagonale de valeur propre de la première matrice de covariance d'échantillon en fonction de la valeur propre maximale théorique (S40); calculer une seconde matrice de covariance d'échantillon en fonction de la matrice diagonale de valeur propre débruitée et d'une matrice composée de vecteurs propres (S50); et calculer la proportion d'investissement de chaque action constitutive en fonction de la seconde matrice de covariance d'échantillon, et générer un portefeuille d'investissement (S60). Au moyen du procédé, le traitement de débruitage d'une matrice de covariance d'échantillon est réalisé, et le risque d'un portefeuille d'investissement est réduit.
PCT/CN2018/107502 2018-06-29 2018-09-26 Procédé et appareil de génération de portefeuille d'investissement, et support d'information lisible par ordinateur WO2020000718A1 (fr)

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CN111898970A (zh) * 2020-06-30 2020-11-06 深圳前海微众银行股份有限公司 一种产品申请资格的认证方法及装置
CN111861711B (zh) * 2020-07-22 2024-06-07 重庆百盐投资(集团)有限公司 资源分配方法及相关产品

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CN103455943A (zh) * 2013-09-02 2013-12-18 深圳市国泰安信息技术有限公司 一种股票或股票投资组合波动率的预测方法、装置
CN105321113A (zh) * 2014-08-04 2016-02-10 同济大学 一种基于宏观因子的压力测试客户端
US20170316507A1 (en) * 2016-04-27 2017-11-02 Anish R. Shah Uncertain utility to improve portfolio selection
CN108090837A (zh) * 2018-02-08 2018-05-29 上海译会信息科技有限公司 一种多种金融产品组合投资策略风险评估方法

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103455943A (zh) * 2013-09-02 2013-12-18 深圳市国泰安信息技术有限公司 一种股票或股票投资组合波动率的预测方法、装置
CN105321113A (zh) * 2014-08-04 2016-02-10 同济大学 一种基于宏观因子的压力测试客户端
US20170316507A1 (en) * 2016-04-27 2017-11-02 Anish R. Shah Uncertain utility to improve portfolio selection
CN108090837A (zh) * 2018-02-08 2018-05-29 上海译会信息科技有限公司 一种多种金融产品组合投资策略风险评估方法

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