Ceci, Claudia; Colaneri, Katia; Cretarola, Alessandra The Föllmer-Schweizer decomposition under incomplete information. (English) Zbl 1394.60055 Stochastics 89, No. 8, 1166-1200 (2017). Summary: In this paper we study the Föllmer-Schweizer decomposition of a square integrable random variable \(\xi\) with respect to a given semimartingale \(S\) under restricted information. Thanks to the relationship between this decomposition and that of the projection of \(\xi\) with respect to the given information flow, we characterize the integrand appearing in the Föllmer-Schweizer decomposition under partial information in the general case where \(\xi\) is not necessarily adapted to the available information level. For partially observable Markovian models where the dynamics of \(S\) depends on an unobservable stochastic factor \(X\), we show how to compute the decomposition by means of filtering problems involving functions defined on an infinite-dimensional space. Moreover, in the case of a partially observed jump-diffusion model where \(X\) is described by a pure jump process taking values in a finite dimensional space, we compute explicitly the integrand in the Föllmer-Schweizer decomposition by working with finite dimensional filters. Finally, we use our achievements in a financial application where we compute the optimal hedging strategy under restricted information for a European put option and provide a comparison with that under complete information. Cited in 3 Documents MSC: 60H05 Stochastic integrals 60G35 Signal detection and filtering (aspects of stochastic processes) 60J75 Jump processes (MSC2010) Keywords:Föllmer-Schweizer decomposition; partial information; nonlinear filtering PDFBibTeX XMLCite \textit{C. Ceci} et al., Stochastics 89, No. 8, 1166--1200 (2017; Zbl 1394.60055) Full Text: DOI arXiv References: [1] J.P. Ansel and C. 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