GKW representation theorem and linear BSDEs under restricted information. An application to risk-minimization

Abstract

In this paper we provide Galtchouk-Kunita-Watanabe representation results in the case where there are restrictions on the available information. This allows to prove existence and uniqueness for linear backward stochastic differential equations driven by a general càdlàg martingale under partial information. Furthermore, we discuss an application to risk-minimization where we extend the results of Föllmer and Sondermann (1986) to the partial information framework and we show how our result fits in the approach of Schweizer (1994).

22 pages

References in corpus (1)

• Variance-optimal hedging for processes with stationary independent increments

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• BSDEs under partial information and financial applications
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• Hedging of unit-linked life insurance contracts with unobservable mortality hazard rate via local risk-minimization
• The Föllmer-Schweizer decomposition under incomplete information