A complete explicit solution to the log-optimal portfolio problem.
\textit{D. Kramkov} and \textit{W. Schachermayer} [ibid. 9, No. 3, 904--950 (1999; Zbl 0967.91017)] proved the existence of log-optimal portfolios under weak assumptions in a very general setting. Explicit solutions to this problem in terms of semimartingale characteristics of the underlying price process were obtained by \textit{T. Goll} and \textit{J. Kallsen} [Stochastic Processes Appl. 89, No. 1, 31--48 (2000)] (the utility being logarithmic). However, the latter paper contains sufficient conditions which are not met in some cases in which optimal solutions are known to exist. The main goal of the present paper is to fill this gap by providing more general conditions which are sufficient as well as necessary. Moreover, earlier results are extended in two respects: first, the authors allow for random convex constraints similar as in [\textit{J. Cvitanić} and \textit{I. Karatzas}, Ann. Appl. Probab. 2, 767--818 (1992; Zbl 0770.90002)]; second, the consumption clock may be stochastic as well (this covers e.g. the case of a random remaining lifetime, which can be interpreted as an old-age pension problem).
scientific article; zbMATH DE number 2005177