I am not so sure about part (b) of the definition of martingale, why the expectation of future fortune is equal to Sn? Is it because Sn+1 depends on Sn? On example (3), how does E(Sn+1|S0, ..., Sn) become E(Sn+Xn+1|Sn)? Also, on the proof of Theorem 10, I don't understand why the indicators are used here?
Reflective
I am really having difficulties understanding this section. In the first paragraph of this section, it says that martingales are used extensively in the modern financial mathematics; but I don't see any connections between them. I feel that maybe because I can't fully understand this section. I hope I can understand them better after the lecture.
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