Geodesic
Log-optimal portfolio without NFLVR: existence, complete characterization, and duality
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 2, pp. 289-308

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This paper addresses the log-optimal portfolio, which is the portfolio with finite expected log-utility that maximizes the expected logarithm utility from terminal wealth, for an arbitrary general semimartingale model. The most advanced literature on this topic elaborates existence and characterization of this portfolio under the no-free-lunch-with-vanishing-risk (NFLVR for short) assumption, while there are many financial models violating NFLVR and admitting the log-optimal portfolio. In this paper, we provide a complete and explicit characterization of the log-optimal portfolio and its associated optimal deflator, give necessary and sufficient conditions for their existence, and elaborate their duality no matter what the market model. Furthermore, our characterization gives an explicit and direct relationship between log-optimal and numéraire portfolios without changing the probability or the numéraire.
Keywords: log-optimal portfolio, numéraire portfolio, log-utility, NUPBR condition, deflator, semimartingale model and characteristics.
Mots-clés : NFLVR condition 
@article{TVP_2022_67_2_a4,
     author = {T. Choulli and S. Yansori},
     title = {Log-optimal portfolio without {NFLVR:} existence, complete characterization, and duality},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {289--308},
     publisher = {mathdoc},
     volume = {67},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_2_a4/}
}
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T. Choulli; S. Yansori. Log-optimal portfolio without NFLVR: existence, complete characterization, and duality. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 2, pp. 289-308. http://geodesic.mathdoc.fr/item/TVP_2022_67_2_a4/