Optimal investment and consumption with unknown parameters

An investment and consumption problem is formulated and its optimal strategy is investigated. We assume the basic binary model, but with unknown parameters. We apply the parametric Bayesian approach to formulate the problem as a sequential stochastic optimization model and use the technique of dynamic programming to characterize the optimal strategy. It is discovered that despite unknown parameters, when the power and logarithmic utility functions are treated, the optimal value function is of the same form of the utility function. The random finite horizon model is formulated as an infinite horizon model. Our results are similar to the ones in the literature having different return functions with constant relative risk aversion.