Computational methods for the stochastic adaptive control for an investment model with transaction fees

A stochastic adaptive control problem is formulated and solved for an investment model that includes stocks and bonds where there is a fee for selling the stocks. It is assumed that the average rate of return of the stocks is unknown. For the known model Taksar, Klass and Assaf (1988) describe the model in terms of the ratio of the wealth in stocks and in bonds and obtain an optimal control when it is desired to maximize the expected rate of growth of the wealth. For this model with the unknown parameter a family of strongly consistent estimators is given in the paper and the certainty equivalence adaptive control is used to solve the stochastic adaptive control problem. The solution is justified by numerically solving the stochastic model for some specific values of the parameters and showing that the family of numerically computed estimates approaches the true unknown parameter value and the family of costs using the numerically computed certainty equivalence adaptive control tends to the optimal cost