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作者：Jaisson, Thibault; Rosenbaum, Mathieu
作者单位：Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：Because of their tractability and their natural interpretations in term of market quantities, Hawkes processes are nowadays widely used in high-frequency finance. However, in practice, the statistical estimation results seem to show that very often, only nearly unstable Hawkes processes are able to fit the data properly. By nearly unstable, we mean that the L-1 norm of their kernel is close to unity. We study in this work such processes for which the stability condition is almost violated. Our...
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作者：Jacob, Emmanuel; Moerters, Peter
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); University of Bath
摘要：We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and spatial clustering gives this model a range of interesting properties. Empirical degree distributions converge to a limit law, which can be a power law with any exponent tau > 2. The average clustering coefficient of the networks converges to a positive lim...
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作者：Trillos, Camilo Andres Garcia
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：We propose an algorithm for approximating the solution of a strongly oscillating SDE, that is, a system in which some ergodic state variables evolve quickly with respect to the other variables. The algorithm profits from homogenization results and consists of an Euler scheme for the slow scale variables coupled with a decreasing step estimator for the ergodic averages of the quick variables. We prove the strong convergence of the algorithm as well as a C.L.T. like limit result for the normaliz...
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作者：Jansen, Sabine; Koenig, Wolfgang; Metzger, Bernd
作者单位：Ruhr University Bochum; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
摘要：An interesting problem in statistical physics is the condensation of classical particles in droplets or clusters when the pair-interaction is given by a stable Lennard Jones-type potential. We study two aspects of this problem. We start by deriving a large deviations principle for the cluster size distribution for any inverse temperature beta is an element of (0, infinity) and particle density rho is an element of (0, rho(cp)) in the thermodynamic limit. Here rho(cp) > 0 is the close packing d...
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作者：Bandyopadhyay, Antar; Sajadi, Farkhondeh
作者单位：Indian Statistical Institute; Indian Statistical Institute Delhi
摘要：In this work we consider a simple SIR infection spread model on a finite population of n agents represented by a finite graph G. Starting with a fixed set of initial infected vertices the infection spreads in discrete time steps, where each infected vertex tries to infect its neighbors with a fixed probability beta is an element of (0, 1), independently of others. It is assumed that each infected vertex dies out after an unit time and the process continues till all infected vertices die out. T...
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作者：Meka, Raghu
作者单位：Microsoft
摘要：We give a polynomial time approximation scheme (PTAS) for computing the supremum of a Gaussian process. That is, given a finite set of vectors V subset of R-d, we compute a (1 + epsilon)-factor approximation to E-X <- N-d [sup(v) (is an element of V) vertical bar < v, X >vertical bar] deterministically in time poly(d) . vertical bar V vertical bar(O epsilon(1)). Previously, only a constant factor deterministic polynomial time approximation algorithm was known due to the work of Ding, Lee and P...
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作者：Keller-Ressel, Martin; Mayerhofer, Eberhard
作者单位：Technical University of Berlin; Dublin City University
摘要：We investigate the maximal domain of the moment generating function of affine processes in the sense of Duffle, Filipovie and Schachermayer [Ann. AppL Probab. 13 (2003) 984-1053], and we show the validity of the affine transform formula that connects exponential moments with the solution of a generalized Riccati differential equation. Our result extends and unifies those preceding it (e.g., Glasserman and Kim [Math. Finance 20 (2010) 1-33], Filipovie and Mayerhofer [Radon Ser. Comput. Appl. Ma...
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作者：Bouchard, Bruno; Nutz, Marcel
作者单位：Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris; Columbia University
摘要：We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of martingale measures. In the arbitrage-free case, we show that optimal superhedging strategies exist for general contingent claims, and that the minimal superhedging price is given by the supremum...
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作者：Fournier, Nicolas
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：We consider the 3D spatially homogeneous Boltzmann equation for (true) hard and moderately soft potentials. We assume that the initial condition is a probability measure with finite energy and is not a Dirac mass. For hard potentials, we prove that any reasonable weak solution immediately belongs to some Besov space. For moderately soft potentials, we assume additionally that the initial condition has a moment of sufficiently high order (8 is enough) and prove the existence of a solution that ...
