You have invested $10\%$ of your wealth in a hedge fund; the other $90\%$ is in cash and there is no time value of money. One year from now the hedge fund will cease operations; it will either fail and give you back only half of your investment, or succeed and give you back 1.85 times your investment. You know that $15\%$ of hedge funds fail every year.
You find a hedge fund evaluation model which, if applied to funds that are going to fail, says they will fail $95\%$ of the time. If the model is applied to funds that will succeed, then it says they will succeed $90\%$ of the time. You run this model on your hedge fund and it says it will fail. You can get your money out now for a $2\%$ exit fee. If you have a logarithmic utility function, should you exit now or stay for the remaining year?
Let $w$ be the $10\%$ wealth that we have invested in the hedge fund. I have set up the utility function if we stay: $$0.95\times\log{0.5w}+0.05\times\log{1.85w}$$ The utility function if we exit: $\log{0.98w}$. Thus we should exit. Can anyone confirm my work? I feel uncertain since I'm not using all the information provided...