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np S_{last} = np   S_0   n\alpha = S_0   n(p   \alpha)
P = \frac{A}{r} \left[ 1 - \frac{1}{(1 r)^n} \right]
{\rm d}r(t) = a(b-r(t)){\rm d}t   \sigma {\rm d}W_t
{\rm d}x(t) = a(x, t){\rm d}t   b(x, t){\rm d}W_t
\widetilde{S} = \frac{pS_0 \alpha S_m}{p \alpha}