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作者：Benjamin, Itai; Makarychev, Yury
作者单位：Weizmann Institute of Science; Toyota Technological Institute - Chicago
摘要：Suppose we sequentially put n balls into n bins. If we put each ball into a random bin then the heaviest bin will contain similar to log n/log log n balls with high probability. However, Azar, Broder, Karlin and Upfal [SIAM J. Comput. 29 (1999) 180-200] showed that if each time we choose two bins at random and put the ball in the least loaded bin among the two, then the heaviest bin will contain only similar to log log n balls with high probability. How much memory do we need to implement this...
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作者：Tong, Xin Thomson; van Handel, Ramon
作者单位：Princeton University
摘要：We consider a bivariate stationary Markov chain (X-n, Y-n)(n >= 0) in a Polish state space, where only the process (Y-n)(n >= 0) is presumed to be observable. The goal of this paper is to investigate the ergodic theory and stability properties of the measure-valued process (Pi(n))(n >= 0), where Pi(n) is the conditional distribution of X-n given Y-0, ... ,Y-n. We show that the ergodic and stability properties of (Pi(n))(n >= 0) are inherited from the ergodicity of the unobserved process (X-n)(...
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作者：Kardaras, Constantinos; Robertson, Scott
作者单位：Boston University; Carnegie Mellon University
摘要：This paper addresses the question of how to invest in a robust growth-optimal way in a market where the instantaneous expected return of the underlying process is unknown. The optimal investment strategy is identified using a generalized version of the principal eigenfunction for an elliptic second-order differential operator, which depends on the covariance structure of the underlying process used for investing. The robust growth-optimal strategy can also be seen as a limit, as the terminal d...
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作者：Feng, Jin; Fouque, Jean-Pierre; Kumar, Rohini
作者单位：University of Kansas; University of California System; University of California Santa Barbara
摘要：In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization problems for nonlinear RIB-type equations where the fast variable lives in a noncompact space. We develop a general argument based on viscosity solutions which we apply to the two regimes studied in the paper. We derive a large deviation principle, and we deduce ...
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作者：Bayraktar, Erhan; Huang, Yu-Jui; Song, Qingshuo
作者单位：University of Michigan System; University of Michigan; City University of Hong Kong
摘要：Our goal is to resolve a problem proposed by Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain probability, as a function of the market configuration and time to maturity. We show that this value function is the smallest nonnegative viscosity supersolution of a nonlinear PDE. As in Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.], we do n...
