论文标题
连续时间对复杂排名依赖性效用代理的一致投资
Consistent Investment of Sophisticated Rank-Dependent Utility Agents in Continuous Time
论文作者
论文摘要
我们在一个完整的连续时间市场中研究投资组合的选择，在该市场中，偏好是由等级依赖性实用程序决定的。由于这种模型本质上是由于潜在的概率加权而不一致的，因此我们研究了寻求（次级完美）个人内部平衡策略的复杂一致计划者的投资行为。我们提供了足够的条件，在该条件下，平衡策略是最终财富的复制投资组合。我们明确地得出了最终的财富概况，事实证明，它的形式与经典的默顿模型中的形式相同，风险过程的市场价格在及时通过确定性功能适当地缩放。我们通过对高度非线性和奇异的普通微分方程的解决方案明确地介绍了这种缩放函数，该方程的存在已建立。最后，我们给出了比例函数小于1小于1的必要条件，该缩放函数与概率加权相对应的有效降低。
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 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 1 corresponding to an effective reduction in risk premium due to probability weighting.
