广义Cox模型下的逐步扩大域流相关问题研究

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, 这里由一个维的布朗运动和一个可积随机 测度驱动; 而第二类投资者具有扩大的信息流, 这里假设是由信息流和广义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, 鞅的分解更复杂和具有一般性.

Progressive Filtration Enlargement in the Generalized Cox Model

We assume that there exist two kinds of investors in the market, the first kind investors, have the market information , which is given by a -dimensional Brownian motion  as well as an integer-valued random measure . The second kind, however, have the information  from the progressive enlargement filtration of  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 . The -decomposition of a -martingale is not trivial in contrast to the class Cox model.