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Exponential Brownian martingale

For every real

c

,

M_{t} = exp (c W_{t} - \frac{1}{2} c^{2} t)

is a martingale. Conditional expectation factors at time

s

because the Gaussian increment

W_{t} - W_{s}

is independent of the past and has exponential moment

e^{c^{2} (t - s) /2}

.

Table of contents 103 3
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  - Power payoff in the Black-Scholes model Risk-neutral measure for the Black-Scholes model 9
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