[ojAlgo-user] Risk Aversion Factor Question

[<bru...@uk...>]

Hi, when looking at the javadoc of the QuadraticSolver class, the 
following can be read:

QuadraticSolver solves optimisation problems of the form: 

min 1/2 [X]T[Q][X] - [C]T[X]
when [AE][X] == [BE]
and [AI][X] <= [BI] 


I wondered how it would be possible to optimise the following problem with 
QuadraticSolver:

min k*[X]T[Q][X] - (1-k)*[R]T[X] where R is the vector of the returns and 
0 <= k <= 1
when [AE][X] == [BE]
and [AI][X] <= [BI] 

Typically I want to either:
- maximise the return for a target volatility [X]T[Q][X] = targetVol
- minimise the volatility for a target return  [R]T[X]       = 
targetReturn

How can I do that with QuadraticSolver?
Here is the code I wrote as an attempt to solve my problem. It gives me 
weights but I am not sure if I have set the problem correctly.

 public boolean solveProblem() {
        Variable[] variables = new Variable[allReturns[0].length];

        //R is the vector of the assets' returns
        //Inequality constraints are between 0 and 1 for the weights

        for (int i = 0; i < variables.length; i++) {
            variables[i] = new Variable("w"+(i+1));
            variables[i].setContributionWeight( R.toBigDecimal(i, 0) );
            variables[i].setLowerLimit("0" );
            variables[i].setUpperLimit("1" ); 
        }

        QuadraticModel quadraticModel = new QuadraticModel(variables);

         //Q is the correlation matrix of the assets' returns
         //The question is: What do I do if I want to set a volatility 
target? How do I specify it?
         // How is it related to the contribution?

        Expression expression = 
quadraticModel.addCorrelationExpression("Variance", Q );
        BigDecimal riskAversion = new BigDecimal("1");
        expression.setContributionWeight(riskAversion.multiply(new 
BigDecimal("0.5")));

        // set balance expression, sum of weights equal to 1
        expression = quadraticModel.addSimpleWeightExpression("Balance");
        expression.setLowerLimit(new BigDecimal("1"));
        expression.setUpperLimit(new BigDecimal("1"));
 
        res = quadraticModel.getDefaultSolver().solve();
        solverState = res.getState();
 
        return solverState == solverState.OPTIMAL;
    }
 

Regards
BF


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