Online one-way trading strategy based on competitive difference analysis
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摘要:
针对交易者事先仅知道价格波动范围的占线单向交易问题，基于 Savage 后悔值准则提出了竞争差分析方法，通过引入一个假想的能够控制价格的“对手”将原来的单人决策问题转化为双人零和博弈问题． 与竞争比分析相比，竞争差分析由于目标函数的数学形式更简单，因而可以直接采用逆向归纳法求解获得使最大后悔值( 竞争差) 最小化的稳健的占线交易策略，并找出对于交易者而言所有可能的最糟糕情况，而不必像竞争比分析那样需要事先猜测最优占线策略的特征; 此外，数值模拟结果表明，基于竞争差分析的占线算法更节省计算时间，且在解决收益最大化问题时不像竞争比分析那样过于保守，一般具有更好的期望绩效．
Abstract:
How to make online trading decisions in one-way trading when only the range of prices in the future is known beforehand? This paper applies Savage’s mini-max regret criterion and proposes a method of compet-itive difference analysis ( CDA) ． The CDA introduces an imaginary adversary who controls the price se-quences，thus transforming the original one-person decision-making problem into a two-person zero-sum game． Compared with the widely used method of competitive ratio analysis ( CＲA) which depends heavily on prior in-tuition，the CDA can directly obtain the optimal online trading strategy and all the possible worst-case scenari-os for the trader via backward induction． In addition，numerical experiments show that the online algorithm based on CDA can save calculation time and that it outperforms the online algorithm based on CＲA when sol-ving revenue-maximization problems because it is less conservative．