Optimal stopping investment in a logarithmic utility-based portfolio selection problem

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.