Continuous time mean-variance-utility portfolio problem and its\n equilibrium strategy

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