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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:  \[n(p)=\pi (-1+2p)p^{-\pi-1}\exp(2\pi(p-1)),\, p < \lt  1,\] \[n(p)=\pi p^{\pi-1},\, p \geq 1.\]