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Kelly bet amount just maximizes log(bankroll). Growth rate, utility, outcomes in series of bets etc. are just interpretations/uses of this fact.
by bluecalm 13y ago
Kelly bet amount just maximizes log(bankroll). Growth rate, utility, outcomes in series of bets etc. are just interpretations/uses of this fact.
- RockyMcNuts 13y agohmmh... nitpick but log utility => maximizing the growth rate, but maximizing the growth rate maximizes utility for many different utility functions, in particular all constant relative risk aversion utility functions, of which log utility is one. so preference for maximizing growth does not imply log utility, could be linear utility too. (under a CRRA utility function, a risky income stream that varies between $1 and $2 gets the same risk aversion discount as one with a similar distribution that varies between $100 and $200, see e.g. http://ocw.mit.edu/courses/economics/14-123-microeconomic-theory-iii-spring-2010/lecture-notes/MIT14_123S10_notes04.pdf http://ocw.mit.edu/courses/economics/14-123-microeconomic-th... )