Improved Pricing on the Stock Market with Trading Agents

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As the tables (1 and 2) show, the standard deviations of the mean values are largeenough to cancel out the pattern of plateaux and valleys I was looking for, i.e., thetests cannot be considered conclusive. Extensive testing, with larger sets of samples,is needed for more definite answers. Still, with the samples I had, the mean valuessupport the hypothesis of plateaux and valleys.To get an idea of whether the standard deviation of the subagents was convergingtowards a finite value or not, I looked at its value for different numbers of samples.Table 3 shows the outcome.Table 3. Standard deviation of subagents for different number of samples. Thesamplesarethesameasthoseintable1and2.Rise of the exchangeThreshold of sale 0.01Threshold of purchase 0.01Fall of the exchangeThreshold of sale 0.01Threshold of purchase 0.0624 samples 26 samples 28 samples0.252 0.245 0.2380.310 0.298 0.288In both cases the standard deviation can be seen to vary a little. It can also beseen to diminish with the number of samples. The evidence is too weak to beconclusive; so I have to keep the question – whether the distribution at hand is fattailedor not – open.4.3 The Trading Agent AlgorithmThis algorithm consists of four subagents, of the type described above, and acomputer generated random function. Only one of the four subagents or the randomfunction is run at a time. The four subagents and the random function come into playaccording to the following scheme. At every juncture, after having run the randomfunction, or one of the subagents has sold its stock, or at the very start of a run of thetrading agent, there is a fifty per cent chance of turning to the computer generatedrandom function, and a fifty per cent chance of running one of the four subagents. Anoverview of the algorithm can be seen in Flowchart 1 (next page). The randomfunction has equal probability of resulting in either a win or a loss. This functionincurs no real loss or gain of capital to the trading agent, as would be the case of thesubagents. If the overall game is set to run one of the four subagents, the subagent ischosen according to the scheme of Table 4 (next page). This means, for example, thatS1 is chosen if both the previous run and the one before that have been losses,incurred by either one of the four subagents or the random function of the computer.In the hope of being able to test for a paradoxical behaviour similar to the one ofthe paradoxical games of Parrondo et al., I gave the subagents S1 and S4 thresholdvalues of winning subagents, and S2 and S3 threshold values of losing subagents.Then I compared the performance of this combined trading agent with the averageperformance of the four subagents. I will discuss this further below.13
Table 4. The choice of subagent.The run before last Last run Subagent chosen for thecoming run, each with itsown pair of limit valuesLoss Loss S1Loss Win S2Win Loss S3Win Win S4Flowchart 1. Overall view of the algorithm at work.Startingpoint of acycleEqualprobability ofchoosingrandomfunction orone of thesubagentsRandom functionEqual probabilityof loss and winChoice ofsubagentdepending onpreviouslosses or wins(Table 4)Subagent S1Subagent S2Subagent S3Subagent S44.4 Results and Conclusions Pertaining to the Trading AgentI tested the trading agent using the landscapes I had obtained (Charts 4 and 5). Iplaced subagents S1 and S4 on the plateau of the falling market and the other two inthe valley. I also tested for three other combinations to see if I could get any newinsights this way. Here I must emphasise that these tests did not test whether thetrading agent would work in a real setting, or not. I used material that I knew wouldgive S1 and S4 good results. The only thing I tested was whether the combined agentwould do better than the average of its constituent subagents would, given that these14
Page 1 and 2: Improved P
Page 3 and 4: mathematical sign that all is not a
Page 5 and 6: If the model corresponds well with
Page 7 and 8: this purpose I designed a subagent
Page 9 and 10: exceeded a threshold value, set bef
Page 11 and 12: Chart 2, 26 Feb 99 - 25 Feb 00, sam
Page 13: Chart 4, Average of 28 samples, 26
Page 17 and 18: separately (compare with results of
Page 19 and 20: interesting to see how much time th
Page 21 and 22: As I have already indicated in a pr
Page 23 and 24: [Blume and Easley, 1990] L. Blume,
Page 25 and 26: B, SHB-ATEL2-B,VOLV-B,WM-B, STE-R,A

Improved Pricing on the Stock Market with Trading Agents

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