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作者：Bielecki, Tomasz R.; Jeanblanc, Monique; Rutkowski, Marek
作者单位：Illinois Institute of Technology; Universite Paris Saclay; University of New South Wales Sydney; Warsaw University of Technology
摘要：In the paper we study dynamics of the arbitrage prices of credit default swaps within a hazard process model of credit risk. We derive these dynamics without postulating that the immersion property is satisfied between some relevant filtrations. These results are then applied so to study the problem of replication of general defaultable claims, including some basket claims, by means of dynamic trading of credit default swaps.
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作者：MacPhee, Iain; Menshikov, Mikhail; Petritis, Dimitri; Popov, Serguei
作者单位：Durham University; Universite de Rennes; Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidade de Sao Paulo
摘要：We consider a polling model with multiple stations, each with Poisson arrivals and a queue of infinite capacity. The service regime is exhaustive and there is Jacksonian feedback of served customers. What is new here is that when the server comes to a station it chooses the service rate and the feedback parameters at random; these remain valid during the whole stay of the server at that station. We give criteria for recurrence, transience and existence of the sth moment of the return time to t...
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作者：Cox, J. Theodore; Perkins, Edwin A.
作者单位：Syracuse University; University of British Columbia
摘要：We show that renormalized two-dimensional Lotka-Volterra models near criticality converge to a super-Brownian motion. This is used to establish long-term survival of a rare type for a range of parameter values near the voter model.
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作者：Pal, Soumik; Pitman, Jim
作者单位：Cornell University; University of California System; University of California Berkeley
摘要：We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long-range behavior of the spacings between the Brownian motions arranged in increasing order. For finitely many Brownian motions interacting in this manner, we characterize drifts for which the family of laws of the vector of spacings is tight and show its convergence to a unique st...
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作者：Sandberg, Oskar
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：Small-world graphs, which combine randomized and structured elements, are seen as prevalent in nature. Jon Kleinberg showed that in some graphs of this type it is possible to route, or navigate, between vertices in few steps even with very little knowledge of the graph itself. In an attempt to understand how such graphs arise we introduce a different criterion for graphs to be navigable in this sense, relating the neighbor selection of a vertex to the hitting probability of routed walks. In se...
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作者：Windisch, David
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider a random walk on the discrete cylinder (7G/NZ)d x 7G, d >_ 3 with drift N-d,, in the 7G-direction and investigate the large N-behavior of the disconnection time TNts, defined as the first time when the trajectory of the random walk disconnects the cylinder into two infinite components. We prove that, as long as the drift exponent a is strictly greater than 1, the asymptotic behavior of TNts remains NZd+o(1) as in the unbiased case considered by Dembo and Sznitman, whereas for a < 1...
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作者：Vath, Vathana Ly; Pham, Huyten; Villeneuve, Stephane
作者单位：Universite Paris Saclay; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Universite Paris Cite; Sorbonne Universite
摘要：We consider a mixed stochastic control problem that arises in Mathematical Finance literature with the study of interactions between dividend policy and investment. This problem combines features of both optimal switching and singular control. We prove that our mixed problem can be decoupled in two pure optimal stopping and singular control problems. Furthermore, we describe the form of the optimal strategy by means of viscosity solution techniques and smooth-fit properties on the correspondin...
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作者：Eichelsbacher, Peter; Reinert, Gesine
作者单位：Ruhr University Bochum; University of Oxford
摘要：Stein's method provides a way of bounding the distance of a probability distribution to a target distribution jL. Here we develop Stein's method for the class of discrete Gibbs measures with a density ev, where V is the energy function. Using size bias couplings, we treat an example of Gibbs convergence for strongly correlated random variables due to Chayes and Klein [Helv. Phys. Acta 67 (1994) 30-42]. We obtain estimates of the approximation to a grand-canonical Gibbs ensemble. As side result...
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作者：Decreusefond, Laurent; Moyal, Pascal
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Universite de Technologie de Compiegne
摘要：In this paper, we present a functional fluid limit theorem and a functional central limit theorem for a queue with an infinity of servers M/GI/infinity. The system is represented by a point-measure valued process keeping track of the remaining processing times of the customers in service. The convergence in law of a sequence of such processes after rescaling is proved by compactness-uniqueness methods, and the deterministic fluid limit is the solution of an integrated equation in the space s' ...
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作者：Bercu, Bernard; Touati, Abderrahmen
作者单位：Centre National de la Recherche Scientifique (CNRS); Inria; CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bordeaux; Universite de Carthage
摘要：We propose several exponential inequalities for self-normalized martingales similar to those established by De la Pena. The keystone is the introduction of a new notion of random variable heavy on left or right. Applications associated with linear regressions, autoregressive and branching processes are also provided.
