The strong predictable representation property in initially enlarged filtrations under the density hypothesis

2015/08/13 by Claudio Fontana, Fontana, Claudio · 1 citation
Economics, Econometrics and Finance · #60G07 #60G44 #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance and Financial Risk Management #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1508.03282

openalex publication_date 2015/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the strong predictable representation property in filtrations initially enlarged with a random variable L. We prove that the strong predictable representation property can always be transferred to the enlarged filtration as long as the classical density hypothesis of Jacod (1985) holds. This generalizes the existing martingale representation results and does not rely on the equivalence between the conditional and the unconditional laws of L. Depending on the behavior of the density process at zero, different forms of martingale representation are established. The results are illustrated in the context of hedging contingent claims under insider information.

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