Determination of Profit Quantification on Kelly Betting Based on Relative Entropy. Issue 4 (4th July 2021)

• Record Type: Journal Article
• Authors: Wu, Mu-En; Lee, Chia-Jung; Chung, Wei-Ho; Yang, Dong-Yuh
• Is Part Of: Quality technology & quantitative management. Volume 18:Issue 4(2021)
• Page Start: 468
• Page End: 483
• Publication Date: 2021-07-04
• Subjects: Kelly criterion -- KL-divergence -- log return -- money management -- optimal fraction; Quality control -- Periodicals; Quality control -- Statistical methods -- Periodicals; Industrial management -- Periodicals; Industrial management; Management -- Research -- Methodology -- Periodicals; Qualitative research -- Periodicals; Management; Quality control; Quality control -- Statistical methods; Periodicals; 658.00721
• DOI: 10.1080/16843703.2021.1903668
• Languages: English
• ISSNs: 1684-3703

Abstract

ABSTRACT: In 1956, John Kelly formulated an optimal strategy, the so-called 'Kelly criterion', for bidding at each step of a favorable game when the odds and probability of winning are known. The Kelly criterion is used to theoretically maximize long-run return. However, in practical situations, it is impossible to play a game for an unlimited time. In this study, we analyze the return of a game when a player must bid after a finite number of time steps. We demonstrate that the logarithm of the return of a game when bidding the optimal fraction (corresponding to the difference between the player's belief probability of the event occurrence and the proportion of real outcomes) for finite-time steps. Moreover, the maximum of the logarithm of the return is achieved when the above two are equal. Finally, a few simulation experiments are conducted for illustrative purposes. We also present an example of a case in stock trading to demonstrate the practicality of this study.