roblem $2.(10$p$)$ At time $t$ we consider a discrete dividend$-$paying stock with spot price $S_t,$ where the stock

pays dividend ${}_{i}0$ at time $t_i,i=1,2,n,$ for $c(S_t,K,T)p(S_t,K,T)S_{t}Kc(S_t,K,T)-p(S_t,K,T)=S_t-{\displaystyle \underset{i=1}{\overset{n}{}}}{}_i{e}^{-r(t_i-t)}-K{e}^{-r(T-t)}r$