The continuous behavior of the numéraire portfolio under small changes in information structure, probabilistic views and investment constraints (Q2267519)

In a financial market, the numéraire portfolio is the log-optimal portfolio (provided that it exists) which has the property that any other wealth process discounted by the log-optimal one, becomes a supermartingale under the historical probability measure; see, e.g., \textit{J. B. J. Long} [``The numéraire portfolio'', J. Financ. Econ. 26, 29--69 (1990)] and \textit{D. Becherer} [Finance Stoch. 5, No. 3, 327--341 (2001; Zbl 0978.91038)]. The numéraire portfolio depends on (a) the information flow available to the acting agents, given by a filtration; (b) by the states of nature given by a probability measure; and (c) a constraint set modeling possible restrictions that agents are facing when applying investment strategies. The author introduces a ``proximity'' concept for the above-mentioned market parameters by defining suitable nodes of convergence. The main result (theorem 1.3) then says that (under suitable conditions) the numéraire portfolio continuously depends (in a rather strong sense) on the above-mentioned market parameters.