Definition

A portfolio is a pair $\phi=((a_{t})_{t\in[0,T]},(b_{t})_{t\in[0,T]})$ of $(\mathcal{F}_{t})_{t\ge 0}$-adapted processes. The value of the portfolio at time $t$ is $$V_{t}(\phi)=a_{t}S_{t}+b_{t}A_{t}$$Hence, at expiration, the value of the portfolio is given by $$V_{T}(\phi)=a_{T}S_{T}+b_{T}A_{T}$$