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Direct comparison approach to Markov systems and its application to portfolio management

Authors Wang, Dexin
Issue Date 2011
Summary This thesis is devoted to the extension of the recently developed direct comparison approach from the performance optimization of finite Markov decision processes (MDPs) to the optimization of continuous-time continuous-state (CTCS) MDPs and partially observable Markov decision processes (POMDPs). Besides the theoretical contributions, we apply the approach to solve some portfolio management problems. First, by revisiting the completion-of-squares technique for the linear quadratic Gaussian problem, we interpret this technique from a new angle, based on which we extend the direct comparison approach to the CTCS MDPs. Without the introduction of dynamic programming, we derive the optimality equation for the long-run average gain-optimal policy. This approach is simple and direct since the derivation for the gain-optimal policy does not depend on the results of either discounted MDPs or finite-horizon MDPs. Second, we propose a practical method to obtain a sub-optimal policy of POMDPs. Based on the internal state, we construct a global-state POMDP whose optimal policy is optimal for the original POMDP in a reduced policy space. Then we solve this global-state POMDP by the direct comparison approach. We find that, if including more information in the internal state, the sub-optimal policy obtained will be closer to the real optimal one. Therefore, the approach provides a tradeoff between policy precision and computation consumption. Furthermore, we apply the approach to portfolio managements in financial engineering. We first consider a market with deterministic parameters and find that the explicit solution of the mean variance portfolio selection in a continuous-time setting can be easily derived by the direct comparison approach. We also consider a more practical market in which the parameters are stochastic and unobservable. We formulate the portfolio management in such an environment as a POMDP optimization and apply the direct comparison approach to solve this POMDP.
Note Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2011
Language English
Format Thesis
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