Tests based on empirical processes

在统计学的大多数应用中，特别是在金融工程中，动态随机模型被假定满足某些假设，主要与它们的概率分布有关。例如，在时间序列中，随机误差项(新息)通常被假定为独立的和/或具有属于某个分布族的分布。拟议研究计划的总体目标是进一步研究基于伪观测的经验过程，伪观测是对来自同一样本的数据的转换，并利用它们来对主要出现在精算学、计量经济学、金融工程和统计学中的模型进行不匹配测试。另一个项目是研究金融中资产的动态配置方法，并将其应用于衍生品定价和对冲基金的复制。

In most applications of statistics, in particular in financial engineering, dynamical stochastic models are assumed to satisfy certain hypotheses, mainly related to their probabilistic distribution. For example, in time series, random error terms (innovations) are often assumed to be independent and/or have a distribution belonging to some family of distributions. The general objective of the proposed research program is to further study empirical processes based on pseudo observations, which are transformations of data from the same sample, and use them to develop tests of lack-of-fit for models appearing mainly in actuarial science, econometry, financial engineering and statistics. Another project consists in studying dynamical allocation methods of assets in finance, with applications to pricing of derivatives and the replication of hedge funds.