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# A METHOD FOR PROVIDING OPTIMAL DECISION MAKING IN FINANCE

IP.com Disclosure Number: IPCOM000015896D
Original Publication Date: 2002-Oct-22
Included in the Prior Art Database: 2003-Jun-21
Document File: 4 page(s) / 158K

IBM

## Abstract

Post Disclosure Text Drawings Enter any additional information relating to this disclosure below: Disclosed is a computer method and a system for providing a solution to the problem of optimizing financial decisions, subject to given financial measurement constraints. The problem can be described as a general (non-convex) min-max problem in the realm of constrained optimization problems. The invention is introduced by first setting forth the following known construct: given a function y f(x,c) c1x1 c2x2, where x is a set of independent variables x {x1,x2}, and x1 x2 are subsets of x, c {c1,c2} is a set of functional parameters, partitioned into two subsets c1 and c2, and y is a dependent variable, it is desired to minimize (over x2) the maximum (over x1) of y, subject to a linear constraint: A12x1+A21x2 b12, where A12, A21 are sub-matrices of matrix A, and b12 is a vector. This means, finding appropriate values for vectors c1 and c2, so as to solve: Min {c2x2 Max c1x1}, subject to: A12x1 +A21x2 b12.

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A METHOD FOR PROVIDING OPTIMAL DECISION MAKING IN FINANCE

Post Disclosure Text & Drawings

Enter any additional information relating to this disclosure below:

Disclosed is a computer method and a system for providing a solution to the problem of optimizing financial decisions, subject to given financial measurement constraints. The problem can be described as a general (non-convex) min-max problem in the realm of constrained optimization problems.

The invention is introduced by first setting forth the following known construct: given a function y = f(x,c) = c1x1 + c2x2, where x is a set of independent variables x = {x1,x2}, and x1 & x2 are subsets of x, c = {c1,c2} is a set of functional parameters, partitioned into two subsets c1 and c2, and y is a dependent variable, it is desired to minimize (over x2) the maximum (over x1) of y, subject to a linear constraint: A12x1+A21x2 <= b12, where A12, A21 are sub-matrices of matrix A, and b12 is a vector. This means, finding appropriate values for vectors c1 and c2, so as to solve: Min {c2x2 + Max c1x1}, subject to: A12x1 +A21x2 <= b12.

This problem is therefore associated with a linear constraint set and a piece-wise linear objective function. Fig. 1 depicts the problem, graphically. The general problem is NP-hard and difficult to resolve in a reasonable time. The usual techniques used in attempting to arrive at an global optimum are Simulated Annealing, Genetic Algorithm or other Monte Carlo type approaches, all of which are slow, cumbersome, and do not guarantee global solution. A novel technique is introduced here that yields a global optimum in the general case of non-convex problem for the set of problems described above. The present invention is cognizant of the aforementioned functional construct. Moreover, the present invention builds upon this known functional construct, but references this known construct to impose upon it novel problems, constraints, and desiderata -- of the following illustrative type.

A typical approach to solving this nonlinear problem would be to parameterize x2 and evaluate the piece-wise linear function g(x ) at every choice of x2. It can be shown that any such search procedure would converge to an extreme point solution of P in finitely many steps. However, the solution to which this procedure converges can at best be a local optimum, as can be shown that function g(x) is concave...