The following lecture talks about the Markowitz Portfolio Optimization problem in convex optimization. Indeed, many variants of this problem exists, but the classical one looks like this

    \begin{equation*}\begin{aligned}& \underset{x}{\text{minimize}}& & x^T \Sigma x \\ & \text{subject to}& & \bar{p}^T x \geq r_{min} \\& & & x \geq 0 \\ & & & 1^T x = 1 \end{aligned}\end{equation*}

where x is an n-sized vector containing the amount of assets to invest in. The vector \bar{p} is the mean of the relative price asset change and the matrix \Sigma is the matrix of variance-covariance of assets. The parameter r_{min} is minimum accepted returns.

Learn more about the above problem and its application to the stock market by watching the above lecture.

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