$ In the "do the job circumstance" you liquidate the portfolio at $t_1$ realising its PnL (let me simplify the notation a tiny bit) To create the two techniques similar it is best to imagine investing/borrowing $PnL_1$ at charge $r$ to ensure it stays during the method till $t_2,.$ At https://pnl34455.activosblog.com/33087724/a-review-of-pnl