Solve the investment allocation problem for Jane and Mark. Their wealth is $1$ Mln$.$ The risky asset returns $20\%$

with probability p

and $4\%$

with probability $1$p

$,$ while the riskless asset gives an interest of $5\%$

$.$ Jane has an utility function UJ$($WJ$)=10+3$ln$($WJ$)$

$,$ while Mark has an utility function UM$($WM$)=5+5$ln$($WM$)$

$.$

Find the optimal allocation of an investment in the risky and in the riskless asset for Jane and for Mark.

Is it the absolute or the relative risk aversion that explains your findings in the question above

If we set the p$=1/2$

$,$ do you expect Jane and Mark to invest more or less in the risky asset, compared to investors characterised by a CRRA utility with parameters of risk aversion $\backslash$eta $=3$

and $\backslash$eta $=2$

$?$

What is the minimum value of the probability p

that makes Jane invest a positive share in the risky asset? And what is this probability for Mark?

What is the critical value of the probability p

for Jane to start borrowing money at the risk$-$less interest rate in order to invest WR$>$W

in the risky asset? And for Mark?