Semi-static completeness and robust pricing by informed investors. (English) Zbl 1415.91249

Acciaio, Beatrice; Larsson, Martin

Ann. Appl. Probab. 27, No. 4, 2270-2304 (2017).

Summary: We consider a continuous-time financial market that consists of securities available for dynamic trading, and securities only available for static trading. We work in a robust framework where a set of non-dominated models is given. The concept of semi-static completeness is introduced: it corresponds to having exact replication by means of semi-static strategies. We show that semi-static completeness is equivalent to an extremality property, and give a characterization of the induced filtration structure. Furthermore, we consider investors with additional information and, for specific types of extra information, we characterize the models that are semi-statically complete for the informed investors. Finally, we provide some examples where robust pricing for informed and uninformed agents can be done over semi-statically complete models.

MSC:

91G10	Portfolio theory
60G44	Martingales with continuous parameter

Keywords:

semi-static completeness; robust finance; extreme points; filtration enlargement; informed pricing