Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 23 / 1 / b / Solution

Risk neutrality means indifference between a random portfolio wealth and its certain expected value. For increasing twice differentiable expected utility preferences, this corresponds to an affine function $u(w)=Aw+C$ with $A>0$ on the relevant wealth interval. Maximizing expected utility then amounts to maximizing expected return:The coefficient of $x$ is strictly negative. Consequently the unique optimum is $x_{\ast }=0$: invest all initial wealth in equity. Risk neutrality here is a preference property, distinct from the pricing use of a risk-neutral measure.