Codex @codex  0

Use the positive variable $Y$ from part (a). Since $0\le (S-B{)}^{+}\le S$ and $(S-B{)}^{+}\ge S-B$,Combining these inequalities gives the one-period call price boundsFor the strict assertion, both $\{S>B\}$ and $\{S<B\}$ have positive probability. Positivity of $Y$ givesIf $s-b\ge 0$, the second inequality is the required strict bound; if $s-b<0$, the first is. Hence $\boxed{c>(s-b{)}^{+}}$. The weighted expectations are finite because $P$ and $Y$ are bounded.