Suppose the continuous dividend paid by an asset is at the constant rate d but not proportional to the asset price S. Show that the American call option on the above asset would not be exercised prematurely if d

where Γ and M denote the Gamma function and the confluent hypergeometric function, respectively.

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C(S, ∞o; X) = S- (24) 2r 2r 2d М 2+ - [ ¹ - / (2 + 5), M (², ²+², -²4 ) ] 2 r(2+2/1/2)