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Abstract Background In this paper, we study the right time for an investor to stop the investment over a given investment horizon so as to obtain as close to the highest possible wealth as possible, according to a Logarithmic utility-maximization objective involving the portfolio in the drift and volatility terms. The problem is formulated as an optimal stopping problem, although it is non-standard in the sense that the maximum wealth involved is not adapted to the information generated over time. Methods By delicate stochastic analysis, the problem is converted to a standard optimal stopping one involving adapted processes. Results Numerical examples shed light on the efficiency of the theoretical results. Conclusion Our investment problem, which includes the portfolio in the drift and volatility terms of the dynamic systems, makes the problem including multi-dimensional financial assets more realistic and meaningful.