$ During the "operate case" you liquidate the portfolio at $t_1$ realising its PnL (let me simplify the notation a tiny bit)WillWill 13344 bronze badges $endgroup$ 4 $begingroup$ Did you not say in the beginning that $V$ is self-funding? In that situation there isn't any Expense to finance it as well as PnL is usually just $V_T-V_t$ among any two t