Bandit Problems with Lévy Processes
Asaf Cohen,Eilon Solan +1 more
TL;DR: In this paper, the authors studied two-armed bandit problems in continuous time, where the risky arm can have two types: High or Low; both types yield stochastic payoffs generated by a Levy process.
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Abstract: Bandit problems model the trade-off between exploration and exploitation in various decision problems. We study two-armed bandit problems in continuous time, where the risky arm can have two types: High or Low; both types yield stochastic payoffs generated by a Levy process. We show that the optimal strategy is a cut-off strategy and we provide an explicit expression for the cut-off and for the optimal payoff.
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References
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Continuous martingales and Brownian motion
Daniel Revuz,Marc Yor +1 more
- 01 Jan 1990
TL;DR: In this article, the authors present a comprehensive survey of the literature on limit theorems in distribution in function spaces, including Girsanov's Theorem, Bessel Processes, and Ray-Knight Theorem.
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Limit Theorems for Stochastic Processes
Jean Jacod,Albert N. Shiryaev +1 more
- 01 Jan 1987
TL;DR: In this article, the General Theory of Stochastic Processes, Semimartingales, and Stochastically Integrals is discussed and the convergence of Processes with Independent Increments is discussed.
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Stochastic differential equations : an introduction with applications
TL;DR: Some Mathematical Preliminaries as mentioned in this paper include the Ito Integrals, Ito Formula and the Martingale Representation Theorem, and Stochastic Differential Equations.
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Lévy Processes and Stochastic Calculus
David Applebaum
- 01 Jan 2004
TL;DR: In this paper, the authors present a general theory of Levy processes and a stochastic calculus for Levy processes in a direct and accessible way, including necessary and sufficient conditions for Levy process to have finite moments.
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