Elementary Proofs on Optimal Stopping

Author: E. Mordecki.

Posted: 29/12/2000, Status: Working paper

Abstract: Elementary proofs of classical theorems on pricing perpetual call and put options in the standard Black-Scholes model are given. The method presented does not rely on stochastic calculus and is also applied to give prices and optimal stopping rules for perpetual call options when the stock is driven by a Lévy process with no positive jumps, and for perpetual put options for stocks driven by a Lévy process with no negative jumps.

Keywords: Optimal stopping, Lévy processes, American options, Derivative pricing, Black-Scholes model.
Classification: JEL: G12, MSC (1991): 60G40

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