[Xinfeng Zhou]A practical Guide to quantitative finance interviews PDF

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if we look at (1+x)^n - (1+nx)

Lagrange 

n is even min = 0 at x = 0 n is odd decreasing (-2, 0) increasing (0, infinity)

so the min for (-2, infinity) is at x = 0 with value 0

this mean (1+x)^n >= 1+nx for x>=-2

 y = ux



!!!

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 

A will win if B lose with an start H this is P(A|H), the probability of A win in this case is 1 - P(A|H)

dy

???????????? wrong figure !!!!!

-x^2/2

bi-linear 双线性

constant 2 here...