@MISC{Mordecki01elementaryproofs, author = {Ernesto Mordecki}, title = {Elementary Proofs on Optimal Stopping}, year = {2001} }

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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 Levy process with no positive jumps, and for perpetual put options for stocks driven by a Levy process with no negative jumps 1 This work was partially written at the Laboratoire de Statistique et Probabilites de l'Universite Paul Sabatier, Toulouse, and beneted from helpful discussion with Walter Moreira. Elementary Proofs on Optimal Stopping Ernesto Mordecki y Facultad de Ciencias. Centro de Matematica. Igua 4225. CP 11400. Montevideo. Uruguay. December 29, 2000 1 Introduction 1.1 Consider a model of a nancial market with two assets, a savings account B = fB t g t0 and a stock S = fS t g t0 . The evolution of B is deterministic, with B t = B 0 e rt ; B 0 = 1; r >...