Optimizing dynamic portfolio selection
In this dissertation, a control-theoretic decision model is proposed for an agent to "optimally" allocate and deploy its financial resources over time among a dynamically changing list of opportunities (e.g., financial assets), in an uncertain market environment. This control-theoretic approach is unique in the sense that it solves the problem at distinct time epochs over a finite time horizon. The solution is a sequence of actions with the objective of optimizing a reward function over that
... nction over that time horizon. While the above problem is quite general, we will focus solely on the problem of dynamic financial portfolio management. The dynamic portfolio model looks at the portfolio as a moving object to achieve a maximal expected utility for a given risk level and time horizon. We tackle this problem using Semi-Markov Decision Processes and develop an efficient solution methodology based on the Q-learning algorithm. The performance of the model is analyzed, and results from the model are compared to a known market index.The "optimal" portfolio management policy is then extended to configurations whereby only incomplete information is available. Furthermore, quality of information and its impact on the decision making process is assessed. Here the market environment is characterized by its volatility and price dynamics. The existence of other agents in the market place, who can act adversarial or collaborative, further complicates the underlying price dynamics. The complexity of interactions among different agents is an important challenge for the dynamic portfolio management problem. We fully examine this challenge using a game-theoretic approach to determine the optimal actions of non-price-taking agents with and without a debt constraint.