Finite time portfolio evolution

Denote the rolled up money-market account by $B_t$ (i.e. $\mathrm{d}B_t = r_t\,B_t\,\mathrm{d}t$). Then

$$\left.\pi_t \right\vert \pi_0 = B_t\int_0^t B_\tau^{-1}\... ...{d}\tau-\Sigma\,\mathrm{d}W_\tau)\right] + B_t\,\pi_0 \quad ,$$ (31)

or, equivalently,

$$\left.\frac{\pi_t}{B_t}-\pi_0 \right\vert \pi_0 = \int_0... ...ambda\,\mathrm{d}\tau-\Sigma\,\mathrm{d}W_\tau)\right]\quad .$$ (32)