Now I'm reading a paper:"alternative characterizations of american put options" , the authors are Carr,Jarrow,Myneni
http://www.math.nyu.edu/research/carrp/papers/pdf/amerput7.pdf
After theorem 1 (in page 4),the author said :
I don't quite understand why the "investor" should hedge the put option when the stock price is below the boundary. I think only the "writer" of the option should hedge,but not the "investor".What's the meaning of this paragraph?
That seems to be a nice paper but I haven't worked through it completely yet.
As I understand it, the goal is to replicate the holding (by an investor) of an European option using an American option, stock and bonds in a self-financing manner. As the value of the underlying changes this requires rebalancing of the option and the bond, i.e. hedging. Since the portfolio is self-financing the value has to be equal. Thus, once you have such a portfolio the value of the American option is the only unknown and it can be derived from the known prices.
Surely, an investor in the traditional sense will just buy the European or American put and not set up a dynamic hedge. Nowadays the authors might have written arbitrageur instead.
