We study portfolio selection in a complete continuous-time market where the preference is dictated by the rank-dependent utility. As such a model is inherently time inconsistent due to the underlying probability weighting, we study the investment behavior of a sophisticated consistent planners who seek (subgame perfect) intra-personal equilibrium strategies. We provide sufficient conditions under which an equilibrium strategy is a replicating portfolio of a final wealth. We derive this final wealth profile explicitly, which turns out to be in the same form as in the classical Merton model with the market price of risk process properly scaled by a deterministic function in time. We present this scaling function explicitly through the solution to a highly nonlinear and singular ordinary differential equation, whose existence of solutions is established. Finally, we give a necessary and sufficient condition for the scaling function to be smaller than one corresponding to an effective reduction in risk premium due to probability weighting.

中文翻译：

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在连续时间内对复杂的等级相关效用代理进行一致投资

我们在一个完整的连续时间市场中研究投资组合选择，其中偏好由依赖于等级的效用决定。由于潜在的概率加权，这种模型在本质上是时间不一致的，我们研究了寻求（子博弈完美）个人内部均衡策略的复杂一致规划者的投资行为。我们提供了充分条件，在该条件下，均衡策略是最终财富的复制投资组合。我们明确地推导出这个最终的财富概况，结果证明它与经典的默顿模型具有相同的形式，风险过程的市场价格由一个确定性函数及时适当地缩放。我们通过对高度非线性和奇异的常微分方程的解来明确地呈现这个缩放函数，其解的存在性成立。最后，我们给出了缩放函数小于对应于由于概率加权有效降低风险溢价的一个充分必要条件。