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 in the literature before.

在本文中，我们提出了一类新的优化问题，在控制投资组合最终风险的均值-方差准则下最大化终端财富和累积消费效用。通过引入投资者整体“幸福感”的概念，将多目标优化问题转化为单目标优化问题，投资者的整体“幸福感”定义为均值-方差准则下的终端财富加总和期望累积效用，然后求解在博弈论框架下。我们设法保持了分析的易处理性；为一组特殊的效用函数找到的封闭形式的解决方案使我们能够讨论一些以前的文献中没有揭示的有趣的最优投资策略。