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作者：Pistorius, Martijn; Stadje, Mitja
作者单位：Imperial College London; Ulm University
摘要：In this paper, we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency, we require that a dynamic deviation measures satisfies a generalised conditional variance formula. We show that, under a domination condition, dynamic deviation measures are characterised as the solutions to a certain class of stochastic differential equations. We establish for any dynamic deviation measure an integr...
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作者：Bai, Lihua; Ma, Jin; Xing, Xiaojing
作者单位：Nankai University; University of Southern California
摘要：In this paper, we study a class of optimal dividend and investment problems assuming that the underlying reserve process follows the Sparre Andersen model, that is, the claim frequency is a renewal process, rather than a standard compound Poisson process. The main feature of such problems is that the underlying reserve dynamics, even in its simplest form, is no longer Markovian. By using the backward Markovization technique, we recast the problem in a Markovian framework with expanded dimensio...
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作者：Tadic, Vladislav B.; Doucet, Arnaud
作者单位：University of Bristol; University of Oxford
摘要：The asymptotic behavior of the stochastic gradient algorithm using biased gradient estimates is analyzed. Relying on arguments based on dynamic system theory (chain-recurrence) and differential geometry (Yomdin theorem and Lojasiewicz inequalities), upper bounds on the asymptotic bias of this algorithm are derived. The results hold under mild conditions and cover a broad class of algorithms used in machine learning, signal processing and statistics.
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作者：Franco, Tertuliano; Neumann, Adriana
作者单位：Universidade Federal da Bahia; Universidade Federal do Rio Grande do Sul
摘要：We consider the one-dimensional symmetric simple exclusion process with a slow bond. In this model, whilst all the transition rates are equal to one, a particular bond, the slow bond, has associated transition rate of value N-1, where N is the scaling parameter. This model has been considered in previous works on the subject of hydrodynamic limit and fluctuations. In this paper, assuming uniqueness for weak solutions of hydrodynamic equation associated to the perturbed process, we obtain dynam...
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作者：Nguyen, Hoi H.
作者单位：University System of Ohio; Ohio State University
摘要：Suppose that A(1),..., A(N) are independent random matrices of size n whose entries are i.i.d. copies of a random variable xi of mean zero and variance one. It is known from the late 1980s that when xi is Gaussian then N-1 log parallel to A(N)... A(1) parallel to converges to log root n as N -> 8. We will establish similar results for more general matrices with explicit rate of convergence. Our method relies on a simple interplay between additive structures and growth of matrices.
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作者：Karnam, Chandrasekhar; Ma, Jin; Zhang, Jianfeng
作者单位：University of Southern California
摘要：In this paper, we investigate possible approaches to study general time-inconsistent optimization problems without assuming the existence of optimal strategy. This leads immediately to the need to refine the concept of time consistency as well as any method that is based on Pontryagin's maximum principle. The fundamental obstacle is the dilemma of having to invoke the Dynamic Programming Principle (DPP) in a time-inconsistent setting, which is contradictory in nature. The main contribution of ...
