this is for holding javascript data
Investment Math added Calculations_The_value_function_is__.md
almost 8 years ago
Commit id: acf25ac6b36092fbd94a487ce9126f8b3769c735
deletions | additions
diff --git a/Calculations_The_value_function_is__.md b/Calculations_The_value_function_is__.md
new file mode 100644
index 0000000..9bc47d3
--- /dev/null
+++ b/Calculations_The_value_function_is__.md
...
# 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:
\[n(p)=\pi (-1+2p)p^{-\pi-1}\exp(2\pi(p-1)),\, p \lt 1,\]
\[n(p)=\pi p^{\pi-1},\, p \geq 1.\]
