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"Pricing formulas for perpetual American options with general payoffs" by Marianito R. Rodrigo

An American option gives the holder the right, but not the obligation, to buy/sell an underlying asset from/to the writer at an agreed strike price at any time on or before the expiry date. Options are mainly used for speculation and hedging. The pricing of options is a fundamental problem in mathematical finance. One of the attractions of options is that they can be used to construct a wide range of trading strategies characterized by different payoff functions. As a preliminary step in the val...
United States Black Scholes Theory Ree Boundary Problem Ellin Transform Ptimal Exercise Boundary Erpetual American Option
Source: uow.edu.au

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