### Abstract

This paper initiates a study into the century-old issue of market predictability from the perspective of computational complexity. We develop a simple agent-based model for a stock market where the agents are traders equipped with simple trading strategies, and their trades together determine the stock prices. Computer simulations show that a basic case of this model is already capable of generating price graphs which are visually similar to the recent price movements of high tech stocks. In the general model, we prove that if there are a large number of traders but they employ a relatively small number of strategies, then there is a polynomial-time algorithm for predicting future price movements with high accuracy. On the other hand, if the number of strategies is large, market prediction becomes complete in two new computational complexity classes CPP and BCPP, where P ^{NP} [&Ogr;(log n)] e BCPP e CPP = PP. These computational completeness results open up a novel possibility that the price graph of a actual stock could be sufficiently deterministic for various prediction goals but appear random to all polynomial-time prediction algorithms.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 745-754 |

Number of pages | 10 |

State | Published - Dec 1 2001 |

Event | 2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States Duration: Apr 30 2001 → May 1 2001 |

### Other

Other | 2001 Operating Section Proceedings, American Gas Association |
---|---|

Country | United States |

City | Dallas, TX |

Period | 4/30/01 → 5/1/01 |

### Fingerprint

### Keywords

- Algorithms
- Management
- Measurement
- Performance
- Theory
- Verification

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 745-754)

}

*Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms.*pp. 745-754, 2001 Operating Section Proceedings, American Gas Association, Dallas, TX, United States, 4/30/01.

**Towards understanding the predictability of stock markets from the perspective of computational complexity.** / Aspnes, James; Fischer, David F.; Fischer, Michael J.; Kao, Ming Yang; Kumar, Alok.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Towards understanding the predictability of stock markets from the perspective of computational complexity

AU - Aspnes, James

AU - Fischer, David F.

AU - Fischer, Michael J.

AU - Kao, Ming Yang

AU - Kumar, Alok

PY - 2001/12/1

Y1 - 2001/12/1

N2 - This paper initiates a study into the century-old issue of market predictability from the perspective of computational complexity. We develop a simple agent-based model for a stock market where the agents are traders equipped with simple trading strategies, and their trades together determine the stock prices. Computer simulations show that a basic case of this model is already capable of generating price graphs which are visually similar to the recent price movements of high tech stocks. In the general model, we prove that if there are a large number of traders but they employ a relatively small number of strategies, then there is a polynomial-time algorithm for predicting future price movements with high accuracy. On the other hand, if the number of strategies is large, market prediction becomes complete in two new computational complexity classes CPP and BCPP, where P NP [&Ogr;(log n)] e BCPP e CPP = PP. These computational completeness results open up a novel possibility that the price graph of a actual stock could be sufficiently deterministic for various prediction goals but appear random to all polynomial-time prediction algorithms.

AB - This paper initiates a study into the century-old issue of market predictability from the perspective of computational complexity. We develop a simple agent-based model for a stock market where the agents are traders equipped with simple trading strategies, and their trades together determine the stock prices. Computer simulations show that a basic case of this model is already capable of generating price graphs which are visually similar to the recent price movements of high tech stocks. In the general model, we prove that if there are a large number of traders but they employ a relatively small number of strategies, then there is a polynomial-time algorithm for predicting future price movements with high accuracy. On the other hand, if the number of strategies is large, market prediction becomes complete in two new computational complexity classes CPP and BCPP, where P NP [&Ogr;(log n)] e BCPP e CPP = PP. These computational completeness results open up a novel possibility that the price graph of a actual stock could be sufficiently deterministic for various prediction goals but appear random to all polynomial-time prediction algorithms.

KW - Algorithms

KW - Management

KW - Measurement

KW - Performance

KW - Theory

KW - Verification

UR - http://www.scopus.com/inward/record.url?scp=35248887420&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35248887420&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:35248887420

SN - 0898714907

SP - 745

EP - 754

BT - Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms

ER -