# mean variance utility function for risk loving person

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?

• This seems like a homework problem. Please show what you tried thus far or this is likely to be closed.
– BKay
Mar 24 '15 at 10:37
• Derived and could show that, utility function for risk loving guy is $E(X)+\frac{r}{2}Var(X);r\geq 0$. Mar 24 '15 at 16:41
• He/She is risky neutral...not a risk lover! Apr 3 '18 at 7:50
• 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. Apr 3 '18 at 11:57

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.