The correct answer is A. Positive slope.
A risk lover is someone who is willing to take on more risk in order to achieve a higher potential return. This means that they are willing to accept a lower expected return in exchange for a higher chance of a higher return.
The utility curve of a risk lover is upward sloping, which means that they are willing to accept a lower expected return in exchange for a higher chance of a higher return.
Option B is incorrect because a risk averter is someone who is not willing to take on more risk. This means that they are not willing to accept a lower expected return in exchange for a higher chance of a higher return.
Option C is incorrect because a risk neutral person is someone who is indifferent to risk. This means that they are willing to accept an expected return that is equal to the risk-free rate.
Option D is incorrect because a risk lover’s utility curve is not concave to the origin.