Enlargement of Filtration with Finance in View by Anna Aksamit & Monique Jeanblanc

Author:Anna Aksamit & Monique Jeanblanc
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

where is given in Proposition 4.5 and . Note that, by the independence hypothesis, B is an -Brownian motion. Hence, exactly the same computations as above can be carried out, it only requires changing to and the intensity of the jumps from to . In particular

The optimal portfolio is given by

The optimal portfolio of the uninformed agent is constant, while the optimal portfolio of the informed agent is time-varying and has a jump whenever the price process jumps.

Since, as expected, , the maximum expected wealth for the informed agent is greater than that of the uninformed agent. In this setting, NFLVR holds: indeed, in this incomplete market, the set of -EMM’s is characterized by the set of the Radon–Nikodym densities which are positive martingales of the form

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