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# 11. [10] The stochastic exponential of a constant, that is, the process & defined by Et = exp xp (aB - 1/2), t for

## 11. [10] The stochastic exponential of a constant, that is, the process & defined by Et = exp xp (aB - 1/2), t for some constant a, is a martingale. a. Prove the above statement directly, that is, by computing E(&|Fs) for s < t. b. Prove it alternatively by appealing to It's formula and properties of stochastic integration.

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