Hello, im new here and I already have some tough questions to ask of y'all. Maybe these problems may be familiar to the mods/helpers of the UK since it was first taught at Cambridge University in 1997.

Down to business:

The partial online book:

A Course in Financial Calculus - Google Book Search

I need help with #4,7,10

#4. (A) Prove lemma 1.3.2.

(B) What happens if we drop the assumption that d < e^rT <u?

#7. Show that if there is no arbitrage in the market, then any portfolio constructed at time zero that exactly replicates a claim C at time T has the same value at time zero.

#10 What is payoff of a forward at expiry? Use risk-neutral pricing to solve the pricing problem for a forward contract.