| Summary: | 博士 === 國立臺灣大學 === 資訊工程學研究所 === 87 === The objective of this thesis is to study the theory of on-line games and an on-line financial trading problem. For the problems of on-line games, we study the theoretical correspondence between competitive analysis and game theory, and also study whether randomization can help the on-line player under various classes of strategies and information structures. The on-line financial problem under study is the buy-and-hold trading problem. We study three variants: (1) the model of symmetric fluctuation ratios, (2) the geometric Brownian motion model, and (3) the model of bounded daily returns. We apply the theoretical results developed for on-line games in the financial problems.
For the theory of on-line game, we have the results: (1) clarifying the assumptions behind the theory of on-line games, (2) establishing the correspondence between equilibrium strategies (game value, respectively) and competitive strategies (optimal competitive ratio, respectively), (3) proving theorems about subgame perfect strategies, (4) deriving a general solution for finite planning games, (5) summarizing methods for estimating the lower bound of the optimal competitive ratios, and (6) proving several theorems on whether randomization can help the on-line player under various classes of strategies and information structures.
For the first variant, we have the results: (1) deriving an optimal randomized threshold algorithm RTA, (2) deriving a tight lower bound, and (3) showing the ratio of RTA''s competitive ratio and the lower bound is O(1), in fact less than 1.8 for a wide range of problem parameters.
For the second variant, we have the results: (1) showing the ratio of expected return is less than 2.2 by simulation, (2) showing the transaction cost is very small.
For the third variant, we have the results: (1) deriving the optimal static trading strategy BAL and the exact optimal competitive ratio, (2) proving uniqueness and optimality, (3) showing that BAL beats the popular dollar-averaging strategy DA, (4) deriving a dynamic strategy SOS that improves BAL for non-worst-case inputs, and (5) performing experiments of BAL and DA for Taiwan''s market in 1997.
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