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fix formula
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Ye Yuan committed Oct 15, 2023
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8 changes: 4 additions & 4 deletions docs/trading/portfolio/CVaR.md
Original file line number Diff line number Diff line change
Expand Up @@ -91,10 +91,10 @@ $$ z_t \geq [-\mathbf{w}^T \mathbf{r}_t - \zeta]^{+} $$
优化问题转化为:

$$\begin{align}
\mathop{\arg \min}_{\mathbf{w}, z_t, \zeta } & & \zeta + \frac{1}{T(1-\alpha)} \sum_{t=1}^T z_t \\
\text{s.t.} & & \mathbf{1}^T \mathbf{w} = 1 \\
& & z_t \geq 0 \\
& & z_t \geq -\mathbf{w}^T \mathbf{r}_t - \zeta
\mathop{\arg \min}_{\mathbf{w}, \mathbf{z}, \zeta } & & \zeta + \frac{1}{T(1-\alpha)} \sum_{t=1}^T z_t & \\
\text{s.t.} & & \mathbf{1}^T \mathbf{w} = 1 & \\
& & z_t \geq 0 & \\
& & z_t \geq -\mathbf{w}^T \mathbf{r}_t - \zeta, & ~~ \text{for} ~~~~ t = 1,2,\dots,T
\end{align}$$

这是一个典型的线性优化问题,可以通过工具包求解。肉眼可以看出,这个优化问题的 __约束条件与采样个数成正比__。因此,计算量可能是一个不可忽略的隐患,在实际生产中值得注意。
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