An Arbitrage Problem

[courtrigrad]

Hello all

I encountered the following problem:

A particular forward contract costs nothing to enter into at time t and obligates the holder to buy the asset for an amount F at expiry, T. The asset pays a divident DS at time t(sub-d), where 0 <= D <= 1 and t <= t(sub-d) <= T. Use an arbitrage argument to find the forward price F(t)

Here is what I did:

I made a chart

Holding Worth Today(t) Worth at maturity(T)

Forward 0 S(T) - F + DT

-Stock -S(t) -S(T)

Cash S(t) + S(t-sub(d)) S(t) + e^(r(T-t))


Total S(t-sub(d)) + S(t) + e^(r(T-t)) - F


I need to solve for F. Am I approaching this problem correctly? Any help would be greatly appreciated!

Thanks

[courtrigrad]

would the dividend cancel out?