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The equality in question follows from the expression for expectation of a log-normal distribution. For example, if $X \stackrel{d}{\sim} N(\mu, \sigma^2)$, then $$ E[e^{a X}] = e^{a \mu + \frac12 a^2 \sigma^2}. $$ This is the reason that CARA/normal or CRRA/log-normal (agent utility/asset return distribution pair) set-ups reduce to the mean-variance case, up ...


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