On Progressive Filtration Expansions with a Process; Applications to Insider Trading

Younes Kchia; Philip Protter

On Progressive Filtration Expansions with a Process; Applications to Insider Trading

Probability 2014-09-18 v2

Authors: Younes Kchia , Philip Protter

Abstract

In this paper we study progressive filtration expansions with c\`adl\`ag processes. Using results from the theory of the weak convergence of $\sigma$ -fields, we first establish a semimartingale convergence theorem. Then we apply it in a filtration expansion with a process setting and provide sufficient conditions for a semimartingale of the base filtration to remain a semimartingale in the expanded filtration. Applications to the expansion of a Brownian filtration are given. The paper concludes with applications to models of insider trading in financial mathematics.

Keywords

progressive filtration expansion càdlàg processes semimartingale convergence weak convergence of sigma-fields brownian filtration insider trading financial mathematics stochastic processes

Cite

@article{arxiv.1403.6323,
  title  = {On Progressive Filtration Expansions with a Process; Applications to Insider Trading},
  author = {Younes Kchia and Philip Protter},
  journal= {arXiv preprint arXiv:1403.6323},
  year   = {2014}
}

Comments

46 pages. arXiv admin note: substantial text overlap with arXiv:1105.1662

On Progressive Filtration Expansions with a Process; Applications to Insider Trading

Abstract

Keywords

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