Statistical tests based on empirical processes

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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, econometrics, financial engineering and statistics. Another project consists in studying dynamical allocation methods of assets in finance, with applications to pricing of derivatives, replication of hedge funds and construction of exchange traded funds (ETF).