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Consider a portfolio which trades so as to keep the proportion of the risky asset at \(0 \lt \pi \lt 1\). A cppi overlay consists in protecting a certain level \(\underline{p}\) with I choose to set at \(1/2\) for illustration. I'll assume that the exposure to the risky asset is decreased linearly from \(\pi\) at \(p=1\) to zero at \(p=1/2\). This gives the following exposure to the portfolio:  \[\pi(p)=\pi-2(1-p),\, p \lt 1,\]  \[\pi(p)=\pi,\, p \geq 1.\] The value function is easily obtained by solving:  \[\frac{dV}{V}=\pi(p)\frac{dp}{p}.\]   This leads to:  \[V(p)=p^{-\pi}\exp(2\pi(p-1)),\, p < 1,\]  \[V(p)=p^{\pi},\, p \geq 1.\]  The trading function is obtained by differentiation as usual:  \[n(p)=\pi(-1+2p)p^{-\pi-1}\exp(2\pi(p-1)),\, p < 1,\]  \[n(p)=\pi p^{\pi-1},\, p \geq 1.\]