  In this paper, we propose a new class of optimization problems, which
maximize the terminal wealth and accumulated consumption utility subject to a
mean variance criterion controlling the final risk of the portfolio. The
multiple-objective optimization problem is firstly transformed into a
single-objective one by introducing the concept of overall "happiness" of an
investor defined as the aggregation of the terminal wealth under the
mean-variance criterion and the expected accumulated utility, and then solved
under a game theoretic framework. We have managed to maintain analytical
tractability; the closed-form solutions found for a set of special utility
functions enable us to discuss some interesting optimal investment strategies
that have not been revealed before in literature.
