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This book proposes a closed-form solution for pricing an American put option on a non-dividend paying stock based on an optimally early-exercise strategy. An American put option should be early exercised when the maximum option premium of early exercise is not less than the value of its European counterpart; otherwise, it should not be early exercised. This paper also shows that Merton (1973)'s formula for pricing a perpetual American put option on a non-dividend paying stock is not perfect and shows such an option's value is equal to its strike price.