Martingale Representation in the Enlargement of the Filtration Generated\n by a Point Process

2019/06/04 by Paolo Di Tella, Di Tella, Paolo, Monique Jeanblanc +1
Mathematics · #Point processes and geometric inequalities #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1906.01208

Abstract

Let X be a point process and let mathbbX denote the filtration\ngenerated by X. In this paper we study martingale representation theorems in\nthe filtration mathbbG obtained as an initial and progressive enlargement\nof the filtration mathbbX. The progressive enlargement is done here by\nmeans of a whole point process H. We do not require further assumptions on\nthe point process H nor on the dependence between X and H. In particular,\nwe recover the special case of the progressive enlargement by a random time\n\τ.\n

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