Question $3$

An insurance company will be required to make a pay$-$out of $$500$ on a

particular risk event, which is likely to occur with a probability of $0\mathrm{.}4.$

The utility for any level of wealth, $w,$ is given by:

$u(w)=4000+-0\mathrm{.}5w$

The insurer's initial level of wealth is $$6000.$ Calculate the minimum

premium the insurer will require in order to take on the risk