# Minimizer for Mean-Variance Portfolio Optimization [closed]

Let $$\lambda \in (0,\infty).$$ Does there exists a minimizer for the set $$\{ -\text{E}[X] + \lambda \text{Var}[X],\; X \in L^2(\Omega,\mathcal{F},P) \} ?$$

## closed as unclear what you're asking by Mark Wildon, Ben McKay, Boris Bukh, Pace Nielsen, Mateusz KwaśnickiJan 12 at 11:26

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## 1 Answer

The answer is no. By considering random variables $$X$$ taking only one real value $$c$$ and then letting $$c\to\infty$$, we see that the infimum of your set is $$-\infty$$ and hence not attained.