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作者：Cuchiero, Christa; Larsson, Martin; Svaluto-Ferro, Sara
作者单位：University of Vienna; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Polynomial jump-diffusions constitute a class of tractable stochastic models with wide applicability in areas such as mathematical finance and population genetics. We provide a full parameterization of polynomial jump-diffusions on the unit simplex under natural structural hypotheses on the jumps. As a stepping stone, we characterize well-posedness of the martingale problem for polynomial operators on general compact state spaces.
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作者：Schumacher, Christoph; Schwarzenberger, Fabian; Veselic, Ivan
作者单位：Dortmund University of Technology
摘要：We consider random fields indexed by finite subsets of an amenable discrete group, taking values in the Banach-space of bounded right-continuous functions. The field is assumed to be equivariant, local, coordinate-wise monotone and almost additive, with finite range dependence. Using the theory of quasi-tilings we prove an uniform ergodic theorem, more precisely, that averages along a Folner sequence converge uniformly to a limiting function. Moreover, we give explicit error estimates for the ...
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作者：Rodosthenous, Neofytos; Zhang, Hongzhong
作者单位：University of London; Queen Mary University London; Columbia University
摘要：We study the optimal stopping of an American call option in a random time-horizon under exponential spectrally negative Levy models. The random time-horizon is modeled as the so-called Omega default clock in insurance, which is the first time when the occupation time of the underlying Levy process below a level y, exceeds an independent exponential random variable with mean 1/q > 0. We show that the shape of the value function varies qualitatively with different values of q and y. In particula...
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作者：Mueller, Marvin S.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Moving boundary problems allow to model systems with phase transition at an inner boundary. Motivated by problems in economics and finance, we set up a price-time continuous model for the limit order book and consider a stochastic and nonlinear extension of the classical Stefan-problem in one space dimension. Here, the paths of the moving interface might have unbounded variation, which introduces additional challenges in the analysis. Working on the distribution space, the Ito-Wentzell formula...
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作者：Forman, Noah; Pal, Soumik; Rizzolo, Douglas; Winkel, Matthias
作者单位：University of Washington; University of Washington Seattle; University of Delaware; University of Oxford
摘要：We establish two results about local times of spectrally positive stable processes. The first is a general approximation result, uniform in space and on compact time intervals, in a model where each jump of the stable process may be marked by a random path. The second gives moment control on the Holder constant of the local times, uniformly across a compact spatial interval and in certain random time intervals. For the latter, we introduce the notion of a Levy process restricted to a compact i...
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作者：Roberts, Matthew, I; Sengul, Bati
作者单位：University of Bath; Bank of America Corporation
摘要：In this paper, we introduce a network model which evolves in time, and study its largest connected component. We consider a process of graphs (G(t) : t is an element of [0, 1]), where initially we start with a critical Erdos-Renyi graph ER(n, 1/n), and then evolve forward in time by resampling each edge independently at rate 1. We show that the size of the largest connected component that appears during the time interval [0, 1] is of order n(2/3) log(1/3)n with high probability. This is in con...
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作者：Avena, Luca; Guldas, Hakan; van der Hofstad, Remco; den Hollander, Frank
作者单位：Leiden University - Excl LUMC; Leiden University; Eindhoven University of Technology
摘要：The mixing time of a random walk, with or without backtracking, on a random graph generated according to the configuration model on n vertices, is known to be of order log n. In this paper, we investigate what happens when the random graph becomes dynamic, namely, at each unit of time a fraction alpha(n) of the edges is randomly rewired. Under mild conditions on the degree sequence, guaranteeing that the graph is locally tree-like, we show that for every epsilon is an element of (0, 1) the eps...
