I post this question here as I didn't receive an answer in the Mathematics community.
I am trying to understand how replicating portfolios can help us determine fair prices.
Suppose we have a 3-year forward contract on 30 assets where each asset pays a dividend of \$15 in one year and \$10 in two years. Revenues are invested in zero coupon bonds maturing at $t=3$ years. The spot price now is $S_0=\$1000$ and the interest rate is 3 % compounded continuously.
Consider a portfolio A with 30 assets. Create a replicating portfolio B using a forward contract on 30 assets with forward price $K$ and bank deposits to determine $K$.
I calculate the future value of the original portfolio A of 30 assets to be $$30S_3+30(10 \cdot e^.03+15\cdot e^.06)$$ at $t=3$ years (the payments are invested in a bank). We do not have $K$ in here since we are not in a contract? I want this to equal the value of portfolio B in order to use the law of one price. The value of the forward contract of B is $30S_3-K$ and thus I need bank deposits to the value of $$30 S_3+30(10 \cdot e^.03+15\cdot e^.06)-(30S_3-K)=K+30(10 \cdot e^.03+15\cdot e^.06).$$Therefore I need to deposit $$Ke^{-3\cdot 0.03}+30\cdot(10 \cdot e^.03+15\cdot e^.06)e^{-3\cdot 0.03}$$ at $t=0$ years. By the law of one price, the portfolios are worth the same at $t=0$ so $$30S_0=Ke^{-3\cdot 0.03}+30\cdot(10 \cdot e^.03+15\cdot e^.06)e^{-3\cdot 0.03}$$ and so I get $$K=e^{3\cdot0.03}\cdot30 \cdot 1000-30\cdot(10 \cdot e^.03+15\cdot e^.06)=\$32038.27$$ Does my approach work?