### Abstract

We answer the question, what should we say about V when we want to gamble on X, and what is it worth? If V = X, we show that every bit of description at rate R is worth a bit of increase Δ(R) in the doubling rate. Thus the efficiency Δ(R)/R is equal to 1. For general V, we provide a single letter characterization for Δ(R). When applied specifically to jointly normal (V,X) with correlation ρ, we find the initial efficiency Δ′ (0) is ρ^{2}. If V and X are Bernoulli random variables connected by a binary symmetric channel with parameter p, the initial efficiency is (1 - 2p)^{2}. We finally show how much increase in doubling rate is possible when the sender can provide R bits of information about V and side information S is available only to the investor.

Original language | English (US) |
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Title of host publication | IEEE International Symposium on Information Theory - Proceedings |

Publisher | IEEE |

Pages | 9 |

Number of pages | 1 |

State | Published - 1995 |

Event | Proceedings of the 1995 IEEE International Symposium on Information Theory - Whistler, BC, Can Duration: Sep 17 1995 → Sep 22 1995 |

### Other

Other | Proceedings of the 1995 IEEE International Symposium on Information Theory |
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City | Whistler, BC, Can |

Period | 9/17/95 → 9/22/95 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Applied Mathematics
- Modeling and Simulation
- Theoretical Computer Science
- Information Systems

### Cite this

*IEEE International Symposium on Information Theory - Proceedings*(pp. 9). IEEE.

**Information efficiency in investment.** / Cover, Thomas M.; Erkip, Elza.

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

*IEEE International Symposium on Information Theory - Proceedings.*IEEE, pp. 9, Proceedings of the 1995 IEEE International Symposium on Information Theory, Whistler, BC, Can, 9/17/95.

}

TY - GEN

T1 - Information efficiency in investment

AU - Cover, Thomas M.

AU - Erkip, Elza

PY - 1995

Y1 - 1995

N2 - We answer the question, what should we say about V when we want to gamble on X, and what is it worth? If V = X, we show that every bit of description at rate R is worth a bit of increase Δ(R) in the doubling rate. Thus the efficiency Δ(R)/R is equal to 1. For general V, we provide a single letter characterization for Δ(R). When applied specifically to jointly normal (V,X) with correlation ρ, we find the initial efficiency Δ′ (0) is ρ2. If V and X are Bernoulli random variables connected by a binary symmetric channel with parameter p, the initial efficiency is (1 - 2p)2. We finally show how much increase in doubling rate is possible when the sender can provide R bits of information about V and side information S is available only to the investor.

AB - We answer the question, what should we say about V when we want to gamble on X, and what is it worth? If V = X, we show that every bit of description at rate R is worth a bit of increase Δ(R) in the doubling rate. Thus the efficiency Δ(R)/R is equal to 1. For general V, we provide a single letter characterization for Δ(R). When applied specifically to jointly normal (V,X) with correlation ρ, we find the initial efficiency Δ′ (0) is ρ2. If V and X are Bernoulli random variables connected by a binary symmetric channel with parameter p, the initial efficiency is (1 - 2p)2. We finally show how much increase in doubling rate is possible when the sender can provide R bits of information about V and side information S is available only to the investor.

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M3 - Conference contribution

AN - SCOPUS:0029179701

SP - 9

BT - IEEE International Symposium on Information Theory - Proceedings

PB - IEEE

ER -