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 $E(X)+\frac{r}{2}Var(X);r\geq 0$. – Pradipta Mar 24 '15 at 16:41
• He/She is risky neutral...not a risk lover! – user17871 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. – BB King 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.