Consider an American call option on an asset that pays discrete dividends at anticipated dates t 1
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Consider an American call option on an asset that pays discrete dividends at anticipated dates t1 2 1,D2, ··· ,Dn, and T = tn+1 be the time of expiration. Show that it is never optimal to exercise the American call at any time prior to expiration if all the discrete dividends are not sufficiently deep, as indicated by the following inequality
![D X[1 er(ti+1-ti)], i=1,2,..., n.](https://dsd5zvtm8ll6.cloudfront.net/images/question_images/1700/5/4/8/295655c4ec76d2da1700548293313.jpg)
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