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OPTIMAL ONLINE ALGORITHMS FOR THE PORTFOLIO SELECTION PROBLEM, BI-DIRECTIONAL TRADING AND -SEARCH WITH INTERRELATED PRICES

机译:组合价格选择,双向交易和搜索的最优在线算法

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In this work we investigate the portfolio selection problem (P1) and bi-directional trading (P2) when prices are interrelated. Zhang et al. (J. Comb. Optim. 23 (2012) 159-166) provided the algorithm UND which solves one variant of P2. We are interested in solutions which are optimal from a worst-case perspective. For P1, we prove the worst-case input sequence and derive the algorithm optimal portfolio for interrelated prices (OPIP). We then prove the competitive ratio and optimality. We use the idea of OPIP to solve P2 and derive the algorithm called optimal conversion for interrelated prices (OCIP). Using OCIP, we also design optimal online algorithms for bi-directional search (P3) called bi-directional UND (BUND) and optimal online search for unknown relative price bounds (RUN). We run numerical experiments and conclude that OPIP and OCIP perform well compared to other algorithms even if prices do not behave adverse.
机译:在这项工作中,我们研究了价格相互关联时的投资组合选择问题(P1)和双向交易(P2)。张等。 J. Comb。Optim。23(2012)159-166)提供了一种算法UND,它可以解决P2的一个变体。从最坏的情况来看,我们对最佳解决方案感兴趣。对于P1,我们证明了最坏情况的输入序列,并推导了相关价格的最佳算法投资组合(OPIP)。然后,我们证明竞争比和最优性。我们使用OPIP的思想来求解P2,并推导称为相互关联价格的最佳转换(OCIP)的算法。使用OCIP,我们还设计了用于双向搜索(P3)的最佳在线算法,称为双向UND(BUND),并针对未知相对价格范围(RUN)设计了最佳在线搜索。我们进行了数值实验,得出结论:即使价格没有不利影响,OPIP和OCIP的性能也优于其他算法。

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