By writing Pn() = e [see (3.5.20)], show that Furthermore, by observing that show that V

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By writing Pn(τ) = e−λτ ()" and Sn = SXne-akt, and considering n!

V(S, t) = P(1) Ex[VBS (n, T)] n=0

[see (3.5.20)], show that

aV  sy + EFEx[vus (5)]  n=0 = -1V - akS. +   Pm(t)Exm+1[VBs(Sm+1, t)]. m=0

Furthermore, by observing that 

Ej[V (JS, t)] = [Pn(7) EXn+1 [VBS (n+1, t)], n=0

show that V (S,τ) satisfies the governing equation (3.5.19). Also, show that V (S,τ) and VBS(S, τ) satisfy the same terminal payoff condition.

2  2 2v 32   2 +E[V(JS,) - V ( S, t )], =   t = T - t + (r - E[J - 1])s- - rV (3.5.19)

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