Hedging behind the decomposition of american put options

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?

• How well your progress with this pager?I'm confused about the equation (12).The author said $B_t$ is only in the premium term,but they didn't replace $S_0$ with $B_0$ in (12),otherwise $B_0$ will appear in the first two term. Apr 4 '15 at 13:54