广义Cox模型下的逐步扩大域流相关问题研究（英文）

Progressive Filtration Enlargement in the Generalized Cox Model

在本文中,我们主要讨论了广义Cox模型的信息流扩大问题.假设在市场中有两类投资者,第一类投资者拥有市场信息F,这里F由一个d维的布朗运动W=(W_1,…,W_d)′和一个可积随机测度μ(du,dy)驱动;而第二类投资者具有扩大的信息流G,这里G假设是由信息流F和广义Cox的模型刻画的违约信息流生成.我们建立和刻画了广义Cox模型并且求给出它的主要性质包括生存过程和违约条件密度.与Cox模型显著区别的是,如果违约由广义Cox模型模型刻画,与Cox模型平凡的结果不同的是,F鞅的G-分解更复杂和具有一般性.

We assume that there exist two kinds of investors in the market, the first kind investors, have the market information F, which is given by a d-dimensional Brownian motion W = （W1,……, Wd） as well as an integer-valued random measure μ（du, dy）. The second kind, however, have the information τ from the progressive enlargement filtration of F by the default time modeled by the so called the generalized Cox model. We characterize this model with a triplet and describe main properties such as the survival process and the conditional density of τ. The G-decomposition of a F-martingale is not trivial in contrast to the class Cox model.