Exponential martingale compensator

For what constant $c$ is the process $M_t = \exp(W_t + c\,t)$ a martingale, where $W_t$ is standard Brownian motion? Give $c$ .

Show hints (2)+

Apply Itô to $f(t,x)=e^{x+ct}$ : include $f_t$ , $f_x$ , and $\tfrac12 f_{xx}$ .
Set the total $dt$ coefficient to zero and solve for $c$ .

Answer

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-0.5

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