Problem $4$ You are given that the annual borrowing and lending rates are rB and rL respectively, both compounded continuously, with rB $>$ rL$.$ We are interested in a forward contract with delivery date T$,$ and the underlying asset is a $($non$-$dividend paying$)$ stock whose current price is S$0.$ Suppose that a fixed transaction cost of A is imposed at the time when one goes long or short a forward contract, and an additional transaction cost of B is charged at time T when the contract is settled. Find the no$-$arbitrage interval for the forward price F$0,$ and verify that arbitrage exists outside the interval. $($You may assume that A $+$ B $$ S$0.)$