homework5Sol.pdf - IEOR-E4707 Spring 2018 Homework 5...

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IEOR-E4707, Spring 2018: Homework 5 Solutions March 29, 2018 Problem 1. Consider a market with one risk-free asset and two stocks whose prices are S ( i ) t = s ( i ) exp { a i t + σW t } , for i = 1 , 2, where W = { W t } t 0 is a one-dimensional Brownian motion, s ( i ) > 0, a 1 6 = a 2 and σ > 0. Prove, in two different ways, that this market has an arbitrage opportunity. Solution:

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