Question: See attached Assume that the function V (S, I, t) satisfies the PDE av av a2 v av + In S at al + 02

See attached

See attached Assume that the function V (S, I, t)See attached Assume that the function V (S, I, t)
Assume that the function V (S, I, t) satisfies the PDE av av a2 v av + In S at al + 02 $2 + rs a$2 - rV = 0. as Consider the change of variables V(S, I, t) = F(y, t), where I+(T - t) InS V= TShow that F(y, t) satisfies the following PDE: OF 02 ( T - t)2 82 F T - tOF + at 2T2 dy2 + r - rF = 0. 2 T dy

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