A Note on the Log-Optimal Portfolio Problem

This note complements Goll and Kallsen (2001) (henceforth GK) in two respects. Firstly, it clarifies the role of self-financing strategies and discounting in the presence of consumption. Moreover, it provides an example which shows that finite expected logarithmic utility does not necessarily imply the existence of an optimal portfolio/consumption pair in the consumption case. Throughout, we use the notation of Jacod and Shiryaev (1987) and Jacod (1979, 1980). The transposed of a vector or matrix x is denoted as x^T and its components by superscripts. Increasing processes are identified with their corresponding Lebesgue-Stieltjes measure.     «

This note complements Goll and Kallsen (2001) (henceforth GK) in two respects. Firstly, it clarifies the role of self-financing strategies and discounting in the presence of consumption. Moreover, it provides an example which shows that finite expected logarithmic utility does not necessarily imply the existence of an optimal portfolio/consumption pair in the consumption case. Throughout, we use the notation of Jacod and Shiryaev (1987) and Jacod (1979, 1980). The transposed of a vector or matri...     »