| Summary: | This thesis is devoted to Markowitz's mean-variance portfolio selection problem in continuous time financial markets, where we aim to minimise the risk of the investment, which is expressed by the variance of the terminal wealth, with a given level of expected return. This thesis consists of an existing literature review and my original extension work. Stochastic linear-quadratic (LQ) control approach and martingale approach are two main methods in dealing with continuous time mean-variance portfolio selection problem. Half of the thesis is allocated to the review of these approaches. The background and motivation, the development, the current status, and the open questions of both approaches are introduced and studied. After the literature review, my extension work is done by martingale approach to find the explicit form of optimal portfolio in an incomplete market when the market parameters are random processes. Speci¯cally, the explicit forms of optimal wealth process and optimal portfolio are obtained for an incomplete market when the market parameters are some simple kind of random processes.
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