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

Claudia Ceci, Alessandra Cretarola and Francesco Russo

may, 2014

Publication type:

Paper in peer-reviewed journals

Journal:

Stochastics and Dynamics, vol. 14(2), pp. 1350019

DOI:

10.1142/S0219493713500196

HAL:

hal-00696616

arXiv:

1205.3726

Keywords :

Backward stochastic differential equations, partial information, Galtchouk-Kunita-Watanabe decomposition, predictable dual projection, 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).

BibTeX:

@article{Cec-Cre-Rus-2014-1,
    author={Claudia Ceci and Alessandra Cretarola and Francesco Russo },
    title={GKW representation theorem and linear BSDEs under restricted 
           information. An application to risk-minimization. },
    doi={10.1142/S0219493713500196 },
    journal={Stochastics and Dynamics },
    year={2014 },
    month={5},
    volume={14(2) },
    pages={1350019},
}