Maple is widely used, which can solve many problems that cannot be solved in traditional problems. Traditional investment performance benchmarks, such as Sharpe ratio, generally return to the distribution of mean and standard deviation, but this is based on the assumption that the distribution is normal. Many modern investment tools, such as hedge funds, have a fat tail in both skewness and kurtosis when they return to distribution. Therefore, traditional tools cannot accurately measure them. Using the tools in Maple can solve such problems.

there is an Omega ratio solution proposed by Shadwick and Keating. This scheme divides the distribution image into two and a half, the area below the target regression value and the area above the target regression value. Omega ratio is the value of the former divided by the latter, and the larger the value, the better.

for a set of discrete regression, the Omega ratio is given by the following formula:

L is the revenue target value, and r is the revenue vector.

The application of this formula finds the weight of assets, which can maximize the Omega ratio of 1 portfolios when considering their simulated monthly income and target income.

this is a global optimization nonconvex problem that requires strict solutions. The transformation of variables (only useful for Omega ratios greater than 1) transforms this optimization into linear programming.

The former uses Maple's global optimization tools, while the latter uses Maple's linear programming features. Omega ratio can combine these two methods. For the data set provided in this paper, both methods give close results.

Regression data and minimum acceptable regression:

Omega ratio:

Target return weight is equal? Scarecrow? Combination:

global optimization:

linear programming:

The description of transforming global optimization into linear programming is as follows:

The above content introduces the process of Maple using Omega ratio to solve regression problems, and it can be seen that the application of Maple in the financial field is also very beneficial. In view of the advantages of Maple in modeling, simulation and calculation, it is very convenient to use it to solve mathematical calculation. If you need to know the application of Maple in science and engineering class, you can refer to how to use MapleSim in science and engineering class.