Hi, I found this question very difficult - I can just about follow the solution but don't think I would have worked it out otherwise.
Please could I check a few things:
How do we know we needed to focus on the discounted asset price? E.g. why couldn't we solve using: E[Bt|Fs] = Bs.
Is it to do with the fact that under Q, risky assets are expected to grow at the risk-free rate and under Q we know that the discounted asset price is a martingale? so these facts suggest we focus on the discounted price? Or should we know for definite it is the discounted asset price to focus on, and if so how do we know that?
How do we know that the probability of not defaulting by time t if it has not defaulted by time s is exp(-lambda(t-s)) and not exp(- int;s to t lambda(s) ds)?
Thanks is advance
Please could I check a few things:
How do we know we needed to focus on the discounted asset price? E.g. why couldn't we solve using: E[Bt|Fs] = Bs.
Is it to do with the fact that under Q, risky assets are expected to grow at the risk-free rate and under Q we know that the discounted asset price is a martingale? so these facts suggest we focus on the discounted price? Or should we know for definite it is the discounted asset price to focus on, and if so how do we know that?
How do we know that the probability of not defaulting by time t if it has not defaulted by time s is exp(-lambda(t-s)) and not exp(- int;s to t lambda(s) ds)?
Thanks is advance