The take-off point for this dissertation is the body of literature in finance and control theory which involves stock-trading strategies based on model-free technical analysis. A salient feature of this line of research is that neither a parameterized model for stock prices nor a behavioral model involving "agents" is used. Many papers in finance documenting the "efficacy" of such trading methods are based on backtesting using historical price data. This reliance on data in lieu of a formal theory explaining successes and failures is one of the main reasons that many in the finance community have criticized this method of trading. In addition, many of these strategies are heuristic in nature which makes them difficult to carry out mathematical analysis. In direct contrast to the approaches above, the main objective of this dissertation is to further the development of a relatively new line of research emerging from control community: using simple ideas involving robust and adaptive control concepts to provide a theory explaining successes and failures of various classes of technically-based trading strategies. In a sense, we seek to "demystify" model-free technical analysis.;Analysis here is carried out under the well-known assumption of an "idealized market". In this setting we analyze the performance of various feedback-based strategies against well-known price benchmarks such as Geometric Brownian Motion. More specifically, we study the statistics for the resulting gain-loss function. We also analyze the expected drawdown in wealth; a widely-used measure of risk. In the presence of skew, we demonstrate that classical mean-variance based analysis can provide a distorted picture of the prospect for success. This can become even more crucial in "mission-critical" applications with the possibility of "model distrust". As an "offshoot" of this research, we introduce a new "conservative" reward-risk pair which not only discounts a possibly-long tail of a distribution but is also largely independent of an individual's risk-preference; i.e., utility function. To this end, the Conservative Expected Value (CEV) and Conservative Semi-Variance (CSV) are formally defined. They are calculated for some of famous probability distribution and some of their most important properties are established.
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