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作者：Kaellblad, Sigrid; Tan, Xiaolu; Touzi, Nizar
作者单位：Technische Universitat Wien; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：We consider the optimal Skorokhod embedding problem (SEP) given full marginals over the time interval [0,1]. The problem is related to the study of extremal martingales associated with a peacock (process increasing in convex order, by Hirsch, Profeta, Roynette and Yor [Peacocks and Associated Martingales, with Explicit Constructions (2011), Springer, Milan]). A general duality result is obtained by convergence techniques. We then study the case where the reward function depends on the maximum ...
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作者：Kabluchko, Zakhar; Marynych, Alexander; Sulzbach, Henning
作者单位：University of Munster; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; McGill University
摘要：We prove an asymptotic Edgeworth expansion for the profiles of certain random trees including binary search trees, random recursive trees and plane-oriented random trees, as the size of the tree goes to infinity. All these models can be seen as special cases of the one-split branching random walk for which we also provide an Edgeworth expansion. These expansions lead to new results on mode, width and occupation numbers of the trees, settling several open problems raised in Devroye and Hwang [A...
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作者：Juengel, Ansgar; Yue, Wen
作者单位：Technische Universitat Wien
摘要：Discrete convex Sobolev inequalities and Beckner inequalities are derived for time-continuous Markov chains on finite state spaces. Beckner inequalities interpolate between the modified logarithmic Sobolev inequality and the Poincare inequality. Their proof is based on the Bakry-Emery approach and on discrete Bochner-type inequalities established by Caputo, Dai Pra and Posta and recently extended by Fathi and Maas for logarithmic entropies. The abstract result for convex entropies is applied t...
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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：Johnson, Peter; Peskir, Goran
作者单位：University of Manchester
摘要：Consider the motion of a Brownian particle that initially takes place in a two-dimensional plane and then after some random/unobservable time continues in the three-dimensional space. Given that only the distance of the particle to the origin is being observed, the problem is to detect the time at which the particle departs from the plane as accurately as possible. We solve this problem in the most uncertain scenario when the random/unobservable time is (i) exponentially distributed and (ii) i...
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作者：Moyal, Pascal; Perry, Ohad
作者单位：Universite de Technologie de Compiegne; Northwestern University
摘要：A matching queue is described via a graph, an arrival process and a matching policy. Specifically, to each node in the graph there is a corresponding arrival process of items, which can either be queued or matched with queued items in neighboring nodes. The matching policy specifies how items are matched whenever more than one matching is possible. Given the matching graph and the matching policy, the stability region of the system is the set of intensities of the arrival processes rendering t...
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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：Bhattacharya, Bhaswar B.; Mukherjee, Sumit
作者单位：University of Pennsylvania; Columbia University
摘要：In this paper, we study the asymptotics of the degree sequence of permutation graphs associated with a sequence of random permutations. The limiting finite-dimensional distributions of the degree proportions are established using results from graph and permutation limit theories. In particular, we show that for a uniform random permutation, the joint distribution of the degree proportions of the vertices labeled [nr(1)], [nr(2)],..., [nr(s)] in the associated permutation graph converges to ind...
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作者：Engelke, Sebastian; Ivanovs, Jevgenijs
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Aarhus University
摘要：Extreme value theory provides an asymptotically justified framework for estimation of exceedance probabilities in regions where few or no observations are available. For multivariate tail estimation, the strength of extremal dependence is crucial and it is typically modeled by a parametric family of spectral distributions. In this work, we provide asymptotic bounds on exceedance probabilities that are robust against misspecification of the extremal dependence model. They arise from optimizing ...
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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...
