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    • 5. 发明申请
    • METHODS AND SYSTEMS FOR ANALYTICAL-BASED MULTIFACTOR MULTIOBJECTIVE PORTFOLIO RISK OPTIMIZATION
    • 基于分析的多因素多元化组合风险优化的方法与系统
    • WO2004086183A2
    • 2004-10-07
    • PCT/US2004/008448
    • 2004-03-19
    • GE FINANCIAL ASSURANCE HOLDINGS, INC.CHAKRABORTY, AnindyaCHALERMKRAIVUTH, Kete, CharlesCLARK, Michael, CraigMESSMER, Richard, PaulKIAER, Carol, LynnBOLLAPRAGADA, Srinivas
    • CHAKRABORTY, AnindyaCHALERMKRAIVUTH, Kete, CharlesCLARK, Michael, CraigMESSMER, Richard, PaulKIAER, Carol, LynnBOLLAPRAGADA, Srinivas
    • G06F
    • G06F1/00
    • The invention provides systems and methods for performing a risk' measure simplification process through matrix manipulation. The method includes defining the change in risk factors; defining portfolio risk sensitivities as Delta and Gamma; restating the change in risk factors in Delta-Gamma formulation, the Delta-Gamma formulation having the factors ΔF's; defining the covariance matrix of ΔF; taking the Cholesky decomposition of the covariance matrix to generate a P transformation matrix; applying the P transformation matrix to Gamma to define a matrix Q k determining the Eigenvalue decomposition of Q k to obtain a matrix of Eigenvectors N; and applying the matrix of Eigenvectors N and the P transformation matrix to evaluate the risk measures. The invention provides systems and methods for determining the allocation of securities in a portfolio. The method includes providing a collection of securities in a portfolio, each security being associated with associated attributes; providing risk factor data related to the portfolio; pooling the securities into a plurality of security clusters based on the attributes associated with each security and the risk factor data, each security being assigned to an security cluster, the pooling being performed using multivariate decision tree processing; processing the security clusters using a nonlinear programming optimizer to generate optimization results; and presenting the optimization results in a risk-return space for determination of a security allocation. The invention provides systems and methods for determining an efficient frontier, which comprises a collection of security allocations in a portfolio, with multiple, conflicting objectives in a multi-factor portfolio problem. The method includes providing a mathematical model of a relaxation of a problem (410); generating a sequence of additional constraints (440); and sequentially applying respective nonlinear risk functions to generate respective adjusted maximum return solutions (606) to obtain an efficient frontier (450).
    • 本发明提供了通过矩阵操纵来执行风险度量简化过程的系统和方法。 该方法包括确定风险因素的变化; 将投资组合风险敏感度定义为Delta和Gamma; 重申Delta-Gamma公式中风险因素的变化,Delta-Gamma公式具有因子DeltaF; 定义DeltaF的协方差矩阵; 采用协方差矩阵的Cholesky分解生成P变换矩阵; 将P变换矩阵应用于Gamma以定义确定Q k的特征值分解以获得特征向量N的矩阵的矩阵Qk; 并应用特征向量N矩阵和P变换矩阵来评估风险度量。 本发明提供用于确定投资组合中证券分配的系统和方法。 该方法包括在投资组合中提供证券集合,每个证券与相关联的属性相关联; 提供与投资组合相关的风险因素数据; 基于与每个安全性相关联的属性和风险因子数据将证券集合到多个安全集群中,每个安全性被分配给安全集群,使用多变量决策树处理来执行该集合; 使用非线性编程优化器处理安全集群以生成优化结果; 并将优化结果呈现在用于确定安全分配的风险回报空间中。 本发明提供了用于确定有效边界的系统和方法,其包括投资组合中的安全分配的集合,在多因素投资组合问题中具有多个冲突的目标。 该方法包括提供问题的松弛的数学模型(410); 产生附加约束的序列(440); 并顺序地应用各自的非线性风险函数以产生相应的调整的最大返回解(606)以获得有效的边界(450)。