The continuous behavior of the numéraire portfolio under small changes in information structure, probabilistic views and investment constraints. (English) Zbl 1188.91203
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., J. B. J. Long [“The numéraire portfolio”, J. Financ. Econ. 26, 29–69 (1990)] and 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.
Reviewer: Klaus Schürger (Bonn)
MSC:
| 91G10 | Portfolio theory |
| 60H99 | Stochastic analysis |
| 60G44 | Martingales with continuous parameter |
| 91B70 | Stochastic models in economics |
| 91B25 | Asset pricing models (MSC2010) |
Keywords:
information; investment constraints; log-utility maximization; mathematical finance; numéraire portfolio; semimartingales; stability; well-posed problemsCitations:
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