Log-Optimal Portfolios for Tree-Structured Wagers


Nigel R. O'Brian


Research Report 2001-11
Date: 17 October 2001


A well-known result of J.L. Kelly gives the log-optimal portfolio for a horse race in terms of each runner's probability of winning and corresponding betting returns. Here Kelly's result is generalised to combinations of `exotic' bets, which depend on runners finishing in specified order. The method takes the form of a exact, recursive algorithm and applies more generally to yield a log-optimal portfolio for any gambling situation where the available bets have a natural tree-type structure.

Key phrases

Log-optimal. portfolio. gambling. bet. wager. Kelly. convexity. Kuhn-Tucker.

AMS Subject Classification (1991)

Primary: 90A09


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