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A quantitative finance related to symmetric random walk, as detailed in picture. 3 . Let ME be a symmetric random walk with Mo = O

A quantitative finance related to symmetric random walk, as detailed in picture.
3 . Let ME be a symmetric random walk with Mo = O and Mr _ _ _ _ _ X;, K 2 1. Xi's are i . i.d. random variables taking value - 1 with probability 1 / 4 and 1 with probability 3 / 4 . Let i'm = inf O : ME = m ]. Find Ele - aTm ] for any a > O

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