Let $X$ denote wealth. The mean variance utility for a risk-averse person is given by $E(X)-\frac{r}{2}Var(X)$ where $r$ is degree of risk-version. $r=0$ implies that person is risk-neutral. How does the mean variance utility function look like for a risk-lover?
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2$\begingroup$ This seems like a homework problem. Please show what you tried thus far or this is likely to be closed. $\endgroup$– BKayCommented Mar 24, 2015 at 10:37
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1$\begingroup$ Derived and could show that, utility function for risk loving guy is $E(X)+\frac{r}{2}Var(X);r\geq 0$. $\endgroup$– PradiptaCommented Mar 24, 2015 at 16:41
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$\begingroup$ He/She is risky neutral...not a risk lover! $\endgroup$– user17871Commented Apr 3, 2018 at 7:50
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$\begingroup$ Well then it sounds like you think you have your answer? Are you just looking for confirmation? If so state that in the question and put your calculations in there too. $\endgroup$– BB KingCommented Apr 3, 2018 at 11:57
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1 Answer
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For a risk lover, r is negative. Making the term $-\frac{r}{2}Var(X)$ positive. Thus, as variance increases, $E(x)-\frac{r}{2}Var(X)$ increases, which means their utility increases.
