Show that Note that By considering the Taylor expansion of n(p ln u/d + ln d) and

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Show that 

lim (n, k, p') = N(d) n where p'ue ueratp and d = In + (r + ) t OT

Note that 

|| 1 - (n, j, p') j - np'  ( P p'(1  p') V In-n(p' In + In d)  a ln np'(1 - p') In 0 < a < 1.

By considering the Taylor expansion of n(p′ ln u/d + ln d) and np′ (1 − p′)(ln u/d)2 in powers of Δt, show that

lim n _n (pln = 2 + Ind) = (r + 2/) + T d nx ~195 2 lim_ap(1  p') (n ) = n - In =ot,

where nΔt = τ .

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