Book suggests that "asset returns are assumed to be serially independent, so wealth is a single state connecting one period to the next". I understand path dependency is lost in case of serial independence but how do all states at a stage collapse to a single state?
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$\begingroup$ Your question is not quite clear to me, would you care to elaborate, please? $\endgroup$ – Ulysses Nov 28 '14 at 15:39
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$\begingroup$ I am unable to understand the statement made in the 2nd paragraph of page 215 of the Book. My understanding is that returns must have a distribution at each stage and so wealth must have a distribution. Hence, there must be a fan like structure connected to another fan like structure. I am struggling to understand the shape of the scenario tree. $\endgroup$ – Kumar Nov 29 '14 at 2:39
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$\begingroup$ I guess it just says that if returns $(r_k)_{k\geq 0}$ are independent, then the wealth $S_n = S_0 \mathrm e^{\sum_k r_k}$ is a Markov process: distribution of $S_{n+1}$ given $S_n$ is same as distribution of $S_{n+1}$ given the whole history $S_0,\dots,S_n$ $\endgroup$ – Ulysses Dec 1 '14 at 9:16
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$\begingroup$ Can you explain that in terms of the shape of the scenario tree in dynamic programming context with stages and states $\endgroup$ – Kumar Dec 1 '14 at 21:40
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$\begingroup$ Not sure what is the scenario tree - can you give an available reference? $\endgroup$ – Ulysses Dec 2 '14 at 6:53
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