We develop and analyze a model of optimal portfolio choice with a finite time horizon T. The investor's objective is to maximize the expected utility of terminal wealth based on partial information generated by stock prices. Rebalancing the portfolio composed of a stock and a bank account incurs transaction costs. This thesis extends the literature by examining the joint impact of partial information and transaction costs on investors' decisions and expected utilities. After estimating the uncertain drift from historical prices, an investor updates the estimate over [0, T] based on partial information. This investor learns about the drift with the Kalman-Bucy filter, which provides a statistically optimal estimate. Three regions of the state space with two free boundaries characterize the optimal portfolio strategy. A numerical algorithm using dynamic programming and a Markov chain approximation solves the model. The existing algorithm with known parameters is time consuming and liable to cause underflow or overflow of the range of values represented. We propose four improvements to overcome the drawbacks. The algorithm with modifications can be applied to the model under partial information according to the separation principle. We define two measures to quantify the losses in utility caused by partial information and transaction costs. Four quantities are introduced to describe investors' trading behaviours. With simulations of stock prices and the drift, the comparative analysis of five market parameters reveals the properties of the model and tests the robustness of the algorithm. Compared with the investors who use erroneous estimates of the drift, the learning investor's portfolio holdings are close to the informed investor's portfolio holdings. The average cost per transaction to the learning investor is the lowest. This investor has these benefits because the filter reduces uncertainty. We discuss the implications for practitioners to highlight the practical contributions of this research.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:577518 |
| Date | January 2011 |
| Creators | Wang, Huamao |
| Publisher | University of Leeds |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://kar.kent.ac.uk/44797/ |
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