Publication Details
Title: Competitive Analysis of Financial Games
Author: R. El-Yaniv, A. Fiat, R. Karp, and G. Turpin
Group: ICSI Technical Reports
Date: September 1992
PDF: ftp://ftp.icsi.berkeley.edu/pub/techreports/1992/tr-92-064.pdf
Overview:
In the unidirectional conversion problem an on-line player is given the task of converting dollars to yen over some period of time. Each day, a new exchange rate is announced, and the player must decide how many dollars to convert. His goal is to minimize the competitive ratio, defined as sup_E P_OPT(E)P_{X}(E), where E ranges over exchange rate sequences, P_OPT(E) is the number of yen obtained by an optimal off-line algorithm, and P_{X}(E) is the number of yen obtained by the on-line algorithm X. We also consider a continuous version of the problem, in which the exchange rate varies over a continuous time interval. The on-line player's a priori information about the fluctuation of exchange rates distinguishes different variants of the problem. For three variants we show that a simple threat-based strategy is optimal for the on-line player and determine its competitive ratio. We also derive and analyze an optimal policy for the on-line player when he knows the probability distribution of the maximum value that the exchange rate will reach. Finally, we consider a bidirectional conversion problem, in which the player may trade dollars for yen or yen for dollars.
Bibliographic Information:
ICSI Technical Report TR-92-064
Bibliographic Reference:
R. El-Yaniv, A. Fiat, R. Karp, and G. Turpin. Competitive Analysis of Financial Games. ICSI Technical Report TR-92-064, September 1992
Author: R. El-Yaniv, A. Fiat, R. Karp, and G. Turpin
Group: ICSI Technical Reports
Date: September 1992
PDF: ftp://ftp.icsi.berkeley.edu/pub/techreports/1992/tr-92-064.pdf
Overview:
In the unidirectional conversion problem an on-line player is given the task of converting dollars to yen over some period of time. Each day, a new exchange rate is announced, and the player must decide how many dollars to convert. His goal is to minimize the competitive ratio, defined as sup_E P_OPT(E)P_{X}(E), where E ranges over exchange rate sequences, P_OPT(E) is the number of yen obtained by an optimal off-line algorithm, and P_{X}(E) is the number of yen obtained by the on-line algorithm X. We also consider a continuous version of the problem, in which the exchange rate varies over a continuous time interval. The on-line player's a priori information about the fluctuation of exchange rates distinguishes different variants of the problem. For three variants we show that a simple threat-based strategy is optimal for the on-line player and determine its competitive ratio. We also derive and analyze an optimal policy for the on-line player when he knows the probability distribution of the maximum value that the exchange rate will reach. Finally, we consider a bidirectional conversion problem, in which the player may trade dollars for yen or yen for dollars.
Bibliographic Information:
ICSI Technical Report TR-92-064
Bibliographic Reference:
R. El-Yaniv, A. Fiat, R. Karp, and G. Turpin. Competitive Analysis of Financial Games. ICSI Technical Report TR-92-064, September 1992