Information geometry of Lévy processes and financial models
Jaehyung Choi
我们探索了Lévy过程的信息几何。作为起点，我们推导了两个Lévy过程之间的α-divergence。随后，从α-divergence出发，计算了与Lévy过程几何相关的Fisher信息矩阵和α-connection。此外，我们还讨论了这种信息几何的统计应用。作为示例，我们研究了与金融建模相关的各种Lévy过程的微分几何结构，包括tempered stable processes、CGMY模型和variance gamma processes。
We explore the information geometry of Lévy processes. As a starting point, we derive the α-divergence between two Lévy processes. Subsequently, the Fisher information matrix and the α-connection associated with the geometry of Lévy processes are computed from the α-divergence. In addition, we discuss statistical applications of this information geometry. As illustrative examples, we investigate the differential-geometric structures of various Lévy processes relevant to financial modeling, inclu...