DYNAMIC OPTIMAL PORTFOLIO WITH LEARNING IN UNOBSERVABLE FACTOR MODELS

Abstract

We formulate a model of risky asset return as a function of an unobservable factor in the capital market. Our Learning Agents are not Merton's, as they have no knowledge of hyperparameters attached in the model at the beginning of investment period. But over the time, Learning Agents will estimate via Bayesian learning mechanism based on the asset return observation. While the learning process updates the posterior distribution, the dimensions in the Dynamic Programing states are growing because we accommodate the entire history of parameters, not just prevailing value. Hence, our Dynamic Programming is cursed by the dimensionality and soon we are hindered by intractability issue. Therefore, to tackle this issue we propose an approximation, which removes the need to enumerate every possible realization via backward recursive calculation. The sub-optimal solution's structure is preserved and it possesses similar structure with Merton framework, except ours is taken with expectation under posterior.