论文标题
在整个市场中可预测的远期绩效过程
Predictable Forward Performance Processes in Complete Markets
论文作者
论文摘要
我们在整个市场中建立了可预测的远期绩效过程（PFPP），这仅在二项式环境中显示。我们的市场模型可以是离散时间或连续的时间模型，投资范围可以是有限的或无限的。我们表明，PFPPS构建的主要步骤是解决一个涉及积分方程的单周期问题，该方程是二项式情况下发现的功能方程的对应物。尽管该积分方程在现有文献中进行了部分研究，但我们使用傅立叶变换提供了一种新的解决方案方法来进行回火分布。我们还为PFPP提供了封闭形式的溶液，具有完全单调的边缘函数，并在此类中建立PFPP的唯一性。我们将结果应用于两种特殊情况。第一个是二项市场，包括将我们的作品与现有文献联系起来。第二个示例考虑了广义的黑色 - choles模型，据我们所知，这是一个新的结果。
We establish existence of Predictable Forward Performance Processes (PFPPs) in complete markets, which has been previously shown only in the binomial setting. Our market model can be a discrete-time or a continuous-time model, and the investment horizon can be finite or infinite. We show that the main step in construction of PFPPs is solving a one-period problem involving an integral equation, which is the counterpart of the functional equation found in the binomial case. Although this integral equation has been partially studied in the existing literature, we provide a new solution method using the Fourier transform for tempered distributions. We also provide closed-form solutions for PFPPs with inverse marginal functions that are completely monotonic and establish uniqueness of PFPPs within this class. We apply our results to two special cases. The first one is the binomial market and is included to relate our work to the existing literature. The second example considers a generalized Black-Scholes model which, to the best of our knowledge, is a new result.
