The Föllmer–Schweizer decomposition under incomplete information. Issue 8 (17th November 2017)

• Record Type: Journal Article
• Authors: Ceci, Claudia; Colaneri, Katia; Cretarola, Alessandra
• Is Part Of: Stochastics. Volume 89:Issue 8(2017)
• Page Start: 1166
• Page End: 1200
• Publication Date: 2017-11-17
• Subjects: Föllmer–Schweizer decomposition -- partial information -- nonlinear filtering; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2017.1290094
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : In this paper we study the Föllmer–Schweizer decomposition of a square integrable random variable with respect to a given semimartingale S under restricted information. Thanks to the relationship between this decomposition and that of the projection of 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 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.