Explicit expressions valid near expiry are derived for the values and the optimal exercise boundaries of American put and call options on assets with dividends. The results depend sensitively on the ratio of the dividend yield rate "D" to the interest rate "r". For "D""r" the put boundary near...

The optimal exercise boundary near the expiration time is determined for an American put option. It is obtained by using Green's theorem to convert the boundary value problem for the price of the option into an integral equation for the optimal exercise boundary. This integral equation is solved...

An optimum checking schedule is one that minimizes the expected cost, which is the sum of the cost of checking and the expected loss due to an undetected failure. The problem is made tractable by supposing that checking is so frequent that it can be described by a continuous density n(t) of...