# 8 6 4 3 as a function of a and b e is the market

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8 6 4 3 as a function of a and b . (e) Is the market complete? Justify.

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7 of 11 4. [15 points] Let W = { W t , t 0 } be a standard Brownian motion. For a fixed constant σ > 0, define the process X = { X t , t 0 } by X t = e σW t E [ e σW t ] . Assume the flow of information is modeled by F = {F t , t 0 } , the filtration generated by W . (a) Give the definition of a continuous-time martingale M = { M t , t 0 } . It is enough to state the martingale property . (b) Compute the conditional expectation of the definition given in (a) to show that X is a martingale. Justify each step.
8 of 11 (c) Using Itˆ o’s formula, show that X is a martingale. Identify clearly the function g ( t, x ) you are using.
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• Spring '09
• idk..
• Financial Markets, Rational pricing, one-period model securities

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