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作者：Matoussi, Anis; Possamai, Dylan; Zhou, Chao
作者单位：Centre National de la Recherche Scientifique (CNRS); Le Mans Universite; Institut Polytechnique de Paris; Ecole Polytechnique; Universite PSL; Universite Paris-Dauphine
摘要：In this article, we build upon the work of Soner, Touzi and Zhang [Probab. Theory Related Fields 153 (2012) 149-190] to define a notion of a second order backward stochastic differential equation reflected on a lower cadlag obstacle. We prove existence and uniqueness of the solution under a Lipschitz-type assumption on the generator, and we investigate some links between our reflected 2BSDEs and nonclassical optimal stopping problems. Finally, we show that reflected 2BSDEs provide a super-hedg...
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作者：Imkeller, Peter; Namachchivaya, N. Sri; Perkowski, Nicolas; Yeong, Hoong C.
作者单位：Humboldt University of Berlin; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We propose a homogenized filter for multiscale signals, which allows us to reduce the dimension of the system. We prove that the nonlinear filter converges to our homogenized filter with rate root epsilon. This is achieved by a suitable asymptotic expansion of the dual of the Zakai equation, and by probabilistically representing the correction terms with the help of BDSDEs.
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作者：Gamarnik, David; Goldberg, David A.
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University System of Georgia; Georgia Institute of Technology
摘要：We consider the FCFS GI/GI/n queue in the so-called Halfin-Whitt heavy traffic regime. We prove that under minor technical conditions the associated sequence of steady-state queue length distributions, normalized by n(1/2), is tight. We derive an upper bound on the large deviation exponent of the limiting steady-state queue length matching that conjectured by Gamarnik and Momcilovic [Adv. in Appl. Probab. 40 (2008) 548-577]. We also prove a matching lower bound when the arrival process is Pois...
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作者：Ott, Curdin
作者单位：University of Bath
摘要：This paper concerns optimal stopping problems driven by the running maximum of a spectrally negative Levy process X. More precisely, we are interested in modifications of the Shepp-Shiryaev optimal stopping problem [Avram, Kyprianou and Pistorius Ann. Appl. Probab. 14 (2004) 215-238; Shepp and Shiryaev Ann. Appl. Probab. 3 (1993) 631-640; Shepp and Shiryaev Theory Probab. Appl. 39 (1993) 103-119]. First, we consider a capped version of the Shepp-Shiryaev optimal stopping problem and provide th...
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作者：Dolinsky, Yan
作者单位：Hebrew University of Jerusalem; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We study the problem of super-replication for game options under proportional transaction costs. We consider a multidimensional continuous time model, in which the discounted stock price process satisfies the conditional full support property. We show that the super-replication price is the cheapest cost of a trivial super-replication strategy. This result is an extension of previous papers (see [Statist. Decisions 27 (2009) 357-369] and [Ann. Appl. Probab. 18 (2008) 491-520]) which considered...
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作者：Hotz, Thomas; Huckemann, Stephan; Le, Huiling; Marron, J. S.; Mattingly, Jonathan C.; Miller, Ezra; Nolen, James; Owen, Megan; Patrangenaru, Vic; Skwerer, Sean
作者单位：Technische Universitat Ilmenau; University of Gottingen; University of Nottingham; University of North Carolina; University of North Carolina Chapel Hill; Duke University; University of Waterloo; State University System of Florida; Florida State University
摘要：Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Frechet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine that is the glued hyperplane, and a central limit theorem (CLT) stating t...
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作者：Lambert, Amaury; Simatos, Florian; Zwart, Bert
作者单位：Sorbonne Universite; Centrum Wiskunde & Informatica (CWI); Vrije Universiteit Amsterdam
摘要：We study the convergence of the M/G/1 processor-sharing, queue length process in the heavy traffic regime, in the finite variance case. To do so, we combine results pertaining to Levy processes, branching processes and queuing theory. These results yield the convergence of long excursions of the queue length processes, toward excursions obtained from those of some reflected Brownian motion with drift, after taking the image of their local time process by the Lamperti transformation. We also sh...
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作者：Radin, Charles; Yin, Mei
作者单位：University of Texas System; University of Texas Austin
摘要：We derive the full phase diagram for a large family of two-parameter exponential random graph models, each containing a first order transition curve ending in a critical point.
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作者：Schied, Alexander
作者单位：University of Mannheim
摘要：We solve a class of control problems with fuel constraint by means of the log-Laplace transforms of J-functionals of Dawson-Watanabe superprocesses. This solution is related to the superprocess solution of quasilinear parabolic PDEs with singular terminal condition. For the probabilistic verification proof, we develop sharp bounds on the blow-up behavior of log-Laplace functionals of J-functionals, which might be of independent interest.
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作者：Penrose, Mathew D.; Yukich, J. E.
作者单位：University of Bath; Lehigh University
摘要：Let Y-i, i >= 1, be i.i.d. random variables having values in an m-dimensional manifold M subset of R-d and consider sums Sigma(n)(i=1) xi (n(1/m)Y(i), {n(1/m)Y(j)}(j=1)(n)), where xi is a real valued function defined on pairs (y, Y), with y epsilon R-d and Y subset of R-d locally finite. Subject to xi satisfying a weak spatial dependence and continuity condition, we show that such sums satisfy weak laws of large numbers, variance asymptotics and central limit theorems. We show that the limit b...
