Numerical methods for the stochastic adaptive control of an investment and consumption model with transaction fees

In this paper an adaptive control problem is formulated and theoretically and numerically solved for an investment and consumption model where the investor´s objective is to maximize the discounted utility. Various utility functions can be used. This model includes different transaction costs for transferring money between stocks and bonds by the purchase or the sale of stocks. The numerical methods for the stochastic adaptive control of this investment and consumption model are a continuation of the work in Duncan et al. (1994) where a model of Taksar-Klass-Assaf (1988) without consumption is considered