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Continuous-Time Red and Black: How to Control a Diffusion to a Goal
A player starts at x in (0, 1) and tries to reach 1. The process ( X t , t (ge) 0) of his positions moves according to a diffusion process (or, more generally, an Ito process) whose infinitesimalExpand
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Continuous-Time Casino Problems
A gambler or an investor seeks to increase his fortune by a given amount before going bankrupt. The problem can be formulated as a stochastic control problem on an interval and is called aExpand
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An extended Fatou equation and continuous-time gambling
Let {Z,, t 0} be an optional stochastic process and let 3 be the directed set of almost-surely-finite stopping times. If lim sup, EZ < oo, then E(lim sup Z, = lim sup, EZ,. This equality is employedExpand
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Gambling theory and stochastic control
Weak approximation of strategies in measurable gambling.
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