\begin{align}\label{eqn:cont_density_pf}
    \pi_t^*(\nu) &= \biggl(\frac{1-q}{\lambda\,q}\biggr)^{\frac{1}{q-1}}\biggl(\psi_t + K_t\biggl(\nu - \frac{L_t}{2\,K_t}\biggr)^2\biggr)^{\frac{1}{q-1}}\,.
\end{align}
