  In this paper, we study the portfolio optimization problem formulated by
Lacker and Soret. They formulate a finite time horizon model that allows agents
to be competitive, measuring their utility not only by their absolute wealth
but also relative performance compared to the average of other agents. While
the finite population or $n$-player game is tractable in some cases, the
authors present the Mean Field Game framework to solve this problem. Here, we
seek to use this framework to clearly detail the optimal investment and
consumption strategies in the CRRA utility case as was briefly outlined in
Lacker and Soret, but also derive a solution in the CARA utility case.
