Optimal insider control and semimartingale decompositions under enlargement of filtration

ABSTRACT

We combine stochastic control methods, white noise analysis, and Hida–Malliavin calculus applied to the Donsker delta functional to obtain explicit representations of semimartingale decompositions under enlargement of filtrations. Some of the expressions are more explicit than previously known. The results are illustrated by examples.

Keywords:

• Enlargement of filtration
• semimartingale decomposition
• optimal inside information control
• Hida–Malliavin calculus, Donsker delta functional

Mathematics Subject Classification:

• 60H40
• 60H07
• 60H05
• 60J75
• 60G48
• 91G80
• 93E20

Acknowledgments

The authors are grateful to Monique Jeanblanc for helpful comments.

Funding

This research was carried out with support of CAS–Centre for Advanced Study, at the Norwegian Academy of Science and Letters, within the research program SEFE, and with support of the Norwegian Research Council, within the research project Challenges in Stochastic Control, Information and Applications (STOCONINF), project number 250768/F20.