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作者：Burzoni, Matte; Frittelli, Marco; Maggis, Marco
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Milan
摘要：In a model-free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semistatic strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path omega is an element of Omega, might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analy...
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作者：Dinh, Vu; Matsen, Frederick A.
作者单位：Fred Hutchinson Cancer Center
摘要：By fixing all parameters in a phylogenetic likelihood model except for one branch length, one obtains a one-dimensional likelihood function. In this work, we introduce a mathematical framework to characterize the shapes of such one-dimensional phylogenetic likelihood functions. This framework is based on analyses of algebraic structures on the space of all frequency patterns with respect to a polynomial representation of the likelihood functions. Using this framework, we provide conditions und...
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作者：Czichowsky, Christoph; Schachermayer, Walter
作者单位：University of London; London School Economics & Political Science; University of Vienna
摘要：processes to be semimartingales, non-semimartingales can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account. In this paper we show, for a class of price processes which are not necessarily semimartingales, the existence of an optimal trading strategy for utility maximisation under transaction costs by establishing the existence of a so-called shadow price. This is a semimartingale price process, taking values in the bid ask spread, such t...
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作者：Anthropelos, Michail; Robertson, Scott; Spiliopoulos, Konstantinos
作者单位：University of Piraeus; Boston University; Boston University
摘要：We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semimartingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well-defined limit, we prove that optimally taken positions become large in absolute value at a specific rate. We draw motivation from and make connections to large deviations theory, and in particular, the celebrated Gartner Ellis theor...
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作者：Last, Guenter; Penrose, Mathew D.; Zuyev, Sergei
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Bath; Chalmers University of Technology; University of Gothenburg
摘要：Consider a Boolean model in R-d with balls of random, bounded radii with distribution F-0, centered at the points of a Poisson process of intensity t > 0. The capacity functional of the infinite cluster Z(infinity) is given by theta(L) (t) = P{Z(infinity) boolean AND L not equal empty set L not equal phi}, defined for each compact L subset of R-d. We prove for any fixed L and F-0 that theta(L) (t) is infinitely differentiable in t, except at the critical value t(c); we give a Margulis-Russo-ty...
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作者：Chetrite, Raphael; Diel, Roland; Lerasle, Matthieu
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Ton Duc Thang University; Ton Duc Thang University
摘要：We consider a Bradley-Terry model in random environment where each player faces each other once. More precisely, the strengths of the players are assumed to be random and we study the influence of their distributions on the asymptotic number of potential winners. First, we prove that under moment and convexity conditions, the asymptotic probability that the best player wins is 1. The convexity condition is natural when the distribution of strengths is unbounded and, in the bounded case, when t...
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作者：Durmus, Alain; Moulines, Eric
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：In this paper, we study a method to sample from a target distribution pi over R-d having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler discretization of the overdamped Langevin stochastic differential equation associated with pi. For both constant and decreasing step sizes in the Euler discretization, we obtain nonasymptotic bounds for the convergence to the target distribution pi in total variation distance. A pa...
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作者：Chatterjee, Sourav; Sen, Sanchayan
作者单位：Stanford University; McGill University
摘要：Kesten and Lee [Ann. AppL Probab. 6 (1996) 495-527] proved that the total length of a minimal spanning tree on certain random point configurations in R-d satisfies a central limit theorem. They also raised the question: how to make these results quantitative? Error estimates in central limit theorems satisfied by many other standard functionals studied in geometric probability are known, but techniques employed to tackle the problem for those functionals do not apply directly to the minimal sp...
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作者：Costantini, Cristina; De Blasi, Pierpaolo; Ethier, Stewart N.; Ruggiero, Matteo; Spano, Dario
作者单位：G d'Annunzio University of Chieti-Pescara; University of Turin; Utah System of Higher Education; University of Utah; University of Warwick
摘要：The two-parameter Poisson-Dirichlet diffusion, introduced in 2009 by Petrov, extends the infinitely-many-neutral-alleles diffusion model, related to Kingman's one-parameter Poisson-Dirichlet distribution and to certain Fleming-Viot processes. The additional parameter has been shown to regulate the clustering structure of the population, but is yet to be fully understood in the way it governs the reproductive process. Here, we shed some light on these dynamics by formulating a K-allele Wright-F...
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作者：Poplavskyi, Mihail; Tribe, Roger; Zaboronski, Oleg
作者单位：University of Warwick
摘要：Let root N + lambda(maX), be the largest real eigenvalue of a random N x N matrix with independent N(0, 1) entries (the real Ginibre matrix). We study the large deviations behaviour of the limiting N -> infinity distribution P[lambda(max) < t] of the shifted maximal real eigenvalue, lambda(max). In particular, we prove that the right tail of this distribution is Gaussian: for t > 0, P[lambda(max) < t] = 1 - 1/4 erfc(t) + O (e(-2t2)). This is a rigorous confirmation of the corresponding result ...
