Question: 1.* 13. In the gambler's ruin problem take b = 1 in (20). Compute i (S {J/Jl ) for a fixed n and show that

1.* 13. In the gambler's ruin problem take b = 1 in (20). Compute i (S {J/\Jl )

for a fixed n and show that {So, S {J/} forms a martingale. Observe that {So, S {J}

does not form a martingale and explain in gambling terms the effect of stopping fJ at n. This example shows why in optional sampling the option may be taken even with the knowledge of the present moment under certain conditions. In the case here the present (namely fJ /\ n) may leave one no choice!

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