Optimal Stopping of Active Portfolio Management

We study an investor¡¯s decision to switch from active portfolio management to passive management. This problem is mathematically modelled by a mixture of a consumption-portfolio selection problem and an optimal stopping problem. We assume that the investor has stochastic differential utility with ambiguity aversion and incurs utility loss from active portfolio management that can be avoided by switching to passive management, and show that she manages actively as long as her level of wealth is above a certain threshold. The threshold wealth level is shown to be an increasing function of both the coefficient of ambiguity aversion and the utility cost of active management.