# How do I find out which form of utility function is being used?

Can someone tell my how i can figure out which type of utility function the following maximization problem has. It is for an overlapping generations model.

$$\underset{x'}{\max} x'\big(E_t (P_{t+1}+δ_{t+1})-(1+r^f)P_t\big) - \tfrac{\gamma}{2} x'Ωx$$
Where: $x'=$ portfolio of shares

$E_t (P_{t+1}+δ_{t+1}) =$ expected future payoff

$\gamma =$ agent i risk aversion

$Ω=$ covariance matrix

• Could you tidy up the notation? Lower script is _{what you want to have as lower index}. E.g.: P_{t+1} May 24 '15 at 21:31

If the random variable of interest is normally distributed with mean $P_{t+1} + \delta_{t+1} - (1+r^f)P_t$ and covariance matrix $\Omega$, and if the agent has constant absolute risk aversion utility, such as $u(w) = 1-e^{-\gamma w}$, then maximizing that utility is equivalent to maximizing mean-variance utility. Here are some details I found with a quick google search.
• Just to clarify wouldn't this be log utility function where $q{z}(R)=R-γ/2R^2$ ? Jun 7 '15 at 13:01