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Title: The reopening of Dubins and Savage casino in the era of diversification Authors:  Isaac Meilijson - Tel Aviv University (Israel) [presenting]
Abstract: In Dynamic Programming, mixed strategies consist of randomizing the choice of actions. In some problems, such as portfolio management,it makes sense to diversify actions rather than choosing among them purely or randomly. Optimal betting in casinos and roulette by a gambler with fixed goal has been studied following Dubins and Savage without the element of diversification (betting simultaneously on different holes of the roulette), once it was proved (Smith's theorem) that diversification doesn't increase the probability of reaching the goal. We question the scope of this finding, that was based on the assumption that the holes on which gamblers can bet are disjoint, such as 1 and BLACK in regular roulette. A counterexample is provided in which holes are nested, such as 1 and RED. Thus, it may be rational for gamblers with fixed goal to place chips on more than one hole at the table. Unlike risk averters, these agents diversify over co-monotone assets (nested holes) but not over antithetic assets (disjoint holes).