Methods and systems for analytical-based multifactor multiobjective portfolio risk optimization
First Claim
1. A method 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 comprising:
- providing a mathematical model of a relaxation of a problem;
generating a sequence of additional constraints; and
sequentially applying respective nonlinear risk functions to generate respective adjusted maximum return solutions to obtain an efficient frontier.
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Accused Products
Abstract
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; generating a sequence of additional constraints; and sequentially applying respective nonlinear risk functions to generate respective adjusted maximum return solutions to obtain an efficient frontier.
172 Citations
22 Claims
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1. A method 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 comprising:
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providing a mathematical model of a relaxation of a problem;
generating a sequence of additional constraints; and
sequentially applying respective nonlinear risk functions to generate respective adjusted maximum return solutions to obtain an efficient frontier. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 21)
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10. A system 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 system comprising:
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a model portion that provides a mathematical model of a relaxation of a problem;
a constraint generation portion that generates a sequence of additional constraints; and
a solution generation portion that sequentially applies respective nonlinear risk functions to generate respective adjusted maximum return solutions to obtain an efficient frontier. - View Dependent Claims (11, 12, 13, 14, 15, 16)
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17. A computer readable medium 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 computer readable medium comprising:
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a first portion that provides a mathematical model of a relaxation of a problem;
a second portion that generates a sequence of additional constraints; and
a third portion that sequentially applies respective nonlinear risk functions to generate respective adjusted maximum return solutions to obtain an efficient frontier. - View Dependent Claims (18, 19)
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20. A method for determining allocations of securities in a portfolio, from which a portfolio manager may select, the method comprising:
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providing a collection of securities in a portfolio, each security being associated with associated attributes;
providing a return function for each security in the portfolio;
applying the return function for each respective security to determine a maximum return solution for the asset portfolio and a first feasible region, the maximum return solution being disposed in the first feasible region, the applying being performed without consideration of risk constraints;
sequentially applying respective nonlinear risk functions to generate respective adjusted maximum return solutions;
generating an efficient frontier in a risk-return space based on the adjusted maximum return solutions; and
wherein the nonlinear risk functions include multiple risk measures.
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22. A method 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 comprising:
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providing a mathematical model of a relaxation of a problem;
generating a sequence of additional constraints;
sequentially applying respective nonlinear risk functions to generate respective adjusted maximum return solutions to obtain an efficient frontier; and
wherein sequentially applying respective nonlinear risk functions to generate respective adjusted maximum return solutions includes solving a linear programming problem to obtain the maximum return; and
wherein sequentially applying respective nonlinear risk functions to generate respective adjusted maximum return solutions further includes;
evaluating a nonlinear risk function at the maximum return solution to determine the risk at that point, which is defined by the maximum return solution;
using a gradient of the nonlinear risk function to determine a tangent plane of that nonlinear risk function at the maximum return solution;
determining a step size based on the desired granularity of the efficient frontier;
shifting the tangent plane by a determined step size to provide a first shifted tangent plane;
applying the first shifted tangent plane as a new linear constraint; and
generating an adjusted feasible region and corresponding maximum return solution.
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Specification