How to Gamble Against All Odds

Speaker
Gilad Bavly
Date
01/01/2014 - 12:00 - 10:00Add To Calendar 2014-01-01 10:00:00 2014-01-01 12:00:00 How to Gamble Against All Odds Abstract: We compare the prediction power of betting strategies (aka martingales) whose wagers take values in different sets of reals. A martingale whose wagers take values in a set A is called an A-martingale. A set of reals B anticipates a set A, if for every A-martingale there is a countable set of B-martingales, such that on every binary sequence on which the A-martingale gains an infinite amount at least one of the B-martingales gains an infinite amount, too. We show that for a wide class of pairs of sets A and B, B anticipates A if and only if A is a subset of the closure of rB, for some r > 0, e.g., when B is well ordered (has no left-accumulation points). Our results answer a question posed by Chalcraft et al. (2012). אוניברסיטת בר-אילן - Department of Economics Economics.Dept@mail.biu.ac.il Asia/Jerusalem public
Affiliation
Tel Aviv University
Abstract

Abstract: We compare the prediction power of betting strategies (aka martingales) whose wagers take values in different sets of reals. A martingale whose wagers take values in a set A is called an A-martingale. A set of reals B anticipates a set A, if for every A-martingale there is a countable set of B-martingales, such that on every binary sequence on which the A-martingale gains an infinite amount at least one of the B-martingales gains an infinite amount, too.
We show that for a wide class of pairs of sets A and B, B anticipates A if and only if A is a subset of the closure of rB, for some r > 0, e.g., when B is well ordered (has no left-accumulation points). Our results answer a question posed by Chalcraft et al. (2012).

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Last Updated Date : 26/12/2013