Ceci, Claudia; Cretarola, Alessandra; Russo, Francesco GKW representation theorem under restricted information. An application to risk-minimization. (English) Zbl 1300.60061 Stoch. Dyn. 14, No. 2, Article ID 1350019, 23 p. (2014). The authors construct a version of the Galtchouk-Kunita-Watanabe representation for a random variable that is measurable w.r.t.the final \(\sigma\)-field \(\mathcal{F}_T\) of some stochastic basis \(\mathbb{F}\), but the decomposition is considered w.r.t.the restricted information, say, \(\mathbb{H}\). Moreover, an explicit characterization of the \(\mathbb{H}\)-adapted integrand process in the decomposition is provided. The concept of \(\mathbb{H}\)-predictable dual projection is introduced to get the main results. As a consequence, the decomposition allows one to construct a solution to special stochastic differential equations whose driver is equal to zero, in a partial information framework. The applications to risk-minimization under restricted information are considered. Reviewer: Yuliya S. Mishura (Kyïv) Cited in 10 Documents MSC: 60G48 Generalizations of martingales 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60H30 Applications of stochastic analysis (to PDEs, etc.) 91G10 Portfolio theory Keywords:Galtchouk-Kunita-Watanabe (GKW) decomposition; equations driven by a càdlàg martingale; partial information; predictable dual projection; risk-minimization PDFBibTeX XMLCite \textit{C. Ceci} et al., Stoch. Dyn. 14, No. 2, Article ID 1350019, 23 p. (2014; Zbl 1300.60061) Full Text: DOI arXiv References: [1] DOI: 10.1016/S0304-4149(01)00131-4 · Zbl 1058.60041 · doi:10.1016/S0304-4149(01)00131-4 [2] DOI: 10.1137/S0040585X97983055 · Zbl 1152.60050 · doi:10.1137/S0040585X97983055 [3] DOI: 10.1080/17442500500488316 · Zbl 1156.91362 · doi:10.1080/17442500500488316 [4] Ceci C., Int. J. Theor. Appl. Fin. 15 pp 24– [5] DOI: 10.1007/978-3-0348-0545-2_17 · Zbl 1281.91140 · doi:10.1007/978-3-0348-0545-2_17 [6] Dellacherie C., Probabilities and Potential B (1982) · Zbl 0494.60002 [7] N. El Karoui and S. J. Huang, Backward Stochastic Differential Equations, eds. N. El Karoui and L. Mazliak (Longman, 1997) pp. 27–36. · Zbl 0887.60064 [8] H. Föllmer and D. Sondermann, Contributions to Mathematical Economics, eds. W. Hildenbrand and A. Mas-Colell (Elsevier, 1986) pp. 205–223. [9] DOI: 10.1111/1467-9965.00090 · Zbl 1022.91023 · doi:10.1111/1467-9965.00090 [10] DOI: 10.1007/s00780-011-0153-0 · Zbl 1259.91055 · doi:10.1007/s00780-011-0153-0 [11] DOI: 10.1080/07362994.2013.741395 · Zbl 1288.60058 · doi:10.1080/07362994.2013.741395 [12] DOI: 10.1214/105051606000000178 · Zbl 1189.91206 · doi:10.1214/105051606000000178 [13] DOI: 10.1007/978-3-662-05265-5 · doi:10.1007/978-3-662-05265-5 [14] Protter P., Applications of Mathematics 21, in: Stochastic Integration and Differential Equations (2004) · Zbl 1041.60005 [15] DOI: 10.1214/aop/1176988611 · Zbl 0814.60041 · doi:10.1214/aop/1176988611 [16] DOI: 10.1111/j.1467-9965.1994.tb00062.x · Zbl 0884.90051 · doi:10.1111/j.1467-9965.1994.tb00062.x [17] DOI: 10.1017/CBO9780511569708.016 · doi:10.1017/CBO9780511569708.016 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.