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How does one take care of constraints when setting up an expected returns maximization model of the following kind:

$y=f(x-r)$ if $z > a$,
$z=g(x-s)$ if $w>b$.

I want to max $E=prob\times y + (1-prob)\times z$. Without the constraints, the first order conditions are easy to solve. How do I introduce the inequality constraints into this maximization problem?

Thanks!

creative
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