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Investment Math edited untitled.md
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# Calculations
The value function is easily obtained by solving:
\[\frac{dV}{V}=\pi(p)\frac{dp}{p}.\]
This leads to:
\[V(p)=p^{-\pi}\exp(2\pi (p-1)),\, p \lt 1,\]
\[V(p)=p^{\pi},\, p \geq 1.\]
The trading function is obtained by differentiation as usual:
\[n(p)=\pi (-1+2p)p^{-\pi-1}\exp(2\pi(p-1)),\, p \lt 1,\]
\[n(p)=\pi p^{\pi-1},\, p \geq 1.\]
