Experimental Analysis of an Online Trading Algorithm

Schmidt, Günter; Mohr, Esther; Kersch, Mike

doi:10.1016/j.endm.2010.05.066

Cited by 20 publications

(5 citation statements)

References 5 publications

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“…Schmidt [29] study the bi-directional conversion problem and compare the performance of Algorithm 11 to the repeated variant of Algorithm 3 on the German DAX30 index for the investment horizon [1998,2007]. Classical (index) buy-and-hold as well as the Dollar Average Strategy are used as benchmarks.…”

Section: Resultsmentioning

confidence: 99%

Online algorithms for conversion problems: A survey

Mohr

Ahmad

Schmidt

2014

Surveys in Operations Research and Management Science

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Section: Resultsmentioning

confidence: 99%

Online algorithms for conversion problems: A survey

Mohr

Ahmad

Schmidt

2014

Surveys in Operations Research and Management Science

Self Cite

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“…This model is relevant where investors are only interested in short term, speculative gains. For the models with known m, M or known ϕ and with one trade, Schmidt et al [11] gave a ϕ-competitive algorithm; it uses the same RP for buying and selling. But consider the Do-Nothing algorithm that makes no trades at all.…”

Section: Previous Results and Related Workmentioning

confidence: 99%

Optimal Online Two-Way Trading with Bounded Number of Transactions

Fung

2018

Algorithmica

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We consider a two-way trading problem, where investors buy and sell a stock whose price moves within a certain range. Naturally they want to maximize their profit. Investors can perform up to k trades, where each trade must involve the full amount. We give optimal algorithms for three different models which differ in the knowledge of how the price fluctuates. In the first model, there are global minimum and maximum bounds m and M. We first show an optimal lower bound of ϕ (where ϕ = M/m) on the competitive ratio for one trade, which is the bound achieved by trivial algorithms. Perhaps surprisingly, when we consider more than one trade, we can give a better algorithm that loses only a factor of ϕ 2/3 (rather than ϕ) per additional trade. Specifically, for k trades the algorithm has competitive ratio ϕ (2k+1)/3. Furthermore we show that this ratio is the best possible by giving a matching lower bound. In the second model, m and M are not known in advance, and just ϕ is known. We show that this only costs us an extra factor of ϕ 1/3 , i.e., both upper and lower bounds become ϕ (2k+2)/3. Finally, we consider the bounded daily return model where instead of a global limit, the fluctuation from one day to the next is bounded, and again we give optimal algorithms, and interestingly one of them resembles common trading strategies that involve stop loss limits.

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“…This model is relevant where investors are only interested in short term, speculative gains. For the models with known m, M or known ϕ and with one trade, Schmidt et al [9] gave a ϕ-competitive algorithm; it uses the same RP for buying and selling. But consider the Do-Nothing algorithm that makes no trades at all.…”

Section: Introductionmentioning

confidence: 99%

Optimal Online Two-Way Trading with Bounded Number of Transactions

Fung

2017

Lecture Notes in Computer Science

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Abstract. We consider a two-way trading problem, where investors buy and sell a stock whose price moves within a certain range. Naturally they want to maximize their profit. Investors can perform up to k trades, where each trade must involve the full amount. We give optimal algorithms for three different models which differ in the knowledge of how the price fluctuates. In the first model, there are global minimum and maximum bounds m and M . We first show an optimal lower bound of ϕ (where ϕ = M/m) on the competitive ratio for one trade, which is the bound achieved by trivial algorithms. Perhaps surprisingly, when we consider more than one trade, we can give a better algorithm that loses only a factor of ϕ 2/3 (rather than ϕ) per additional trade. Specifically, for k trades the algorithm has competitive ratio ϕ (2k+1)/3 . Furthermore we show that this ratio is the best possible by giving a matching lower bound. In the second model, m and M are not known in advance, and just ϕ is known. We show that this only costs us an extra factor of ϕ 1/3 , i.e., both upper and lower bounds become ϕ (2k+2)/3 . Finally, we consider the bounded daily return model where instead of a global limit, the fluctuation from one day to the next is bounded, and again we give optimal algorithms, and interestingly one of them resembles common trading strategies that involve stop loss limits.

show abstract

Experimental Analysis of an Online Trading Algorithm

Cited by 20 publications

References 5 publications

Online algorithms for conversion problems: A survey

Online algorithms for conversion problems: A survey

Optimal Online Two-Way Trading with Bounded Number of Transactions

Optimal Online Two-Way Trading with Bounded Number of Transactions

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