论文标题
随机申请随机居住后生活的代表
Representation for martingales living after a random time with applications
论文作者
论文摘要
我们的财务环境包括一个具有两个信息流的市场模型。最小的流量F是所有代理商都可以使用的“公共”信息流，而较大的流量G则具有有关发生随机时间t的其他信息。此随机时间可以对信用风险或人寿保险中的默认时间建模。因此，过滤g是f与T的逐渐扩大。在该框架中，在对这对的一些轻度假设（f，t）下，我们明确地描述了如何以f-local martingale和T的t表示。 Martingales的生活“在T之后”。这些结果的应用在G下所有缩小器的明确参数化中均已完全详细阐述。在跳跃扩散模型和离散时间市场模型的情况下说明了结果。
Our financial setting consists of a market model with two flows of information. The smallest flow F is the "public" flow of information which is available to all agents, while the larger flow G has additional information about the occurrence of a random time T. This random time can model the default time in credit risk or death time in life insurance. Hence the filtration G is the progressive enlargement of F with T. In this framework, under some mild assumptions on the pair (F, T), we describe explicitly how G-local martingales can be represented in terms of F-local martingale and parameters of T. This representation complements Choulli, Daveloose and Vanmaele \cite{ChoulliDavelooseVanmaele} to the case when martingales live "after T". The application of these results to the explicit parametrization of all deflators under G is fully elaborated. The results are illustrated on the case of jump-diffusion model and the discrete-time market model.
