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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...
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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：Gravner, Janko; Sivakoff, David
作者单位：University of California System; University of California Davis; University System of Ohio; Ohio State University
摘要：Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic puzzle graph by using connectivity properties of a random people graph on the same set of vertices. We presume the Erdos-Renyi people graph with edge probability p and investigate the probability that the puzzle is solved, that is, that the process eventually produces a single cluster. In some generality, for puzzle graphs with N vertices of degrees about D (in the appropriate sense), this pr...
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作者：Caravenna, Francesco; Sun, Rongfeng; Zygouras, Nikos
作者单位：University of Milano-Bicocca; National University of Singapore; University of Warwick
摘要：We consider disordered systems of a directed polymer type, for which disorder is so-called marginally relevant. These include the usual (short-range) directed polymer model in dimension (2 + 1), the long-range directed polymer model with Cauchy tails in dimension (1 + 1) and the disordered pinning model with tail exponent 1/2. We show that in a suitable weak disorder and continuum limit, the partition functions of these different models converge to a universal limit: a log-normal random field ...
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作者：Clement, Dombry; Landy, Rabehasaina
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Marie et Louis Pasteur
摘要：A high order expansion of the renewal function is provided under the assumption that the inter-renewal time distribution is light tailed with finite moment generating function g on a neighborhood of 0. This expansion relies on complex analysis and is expressed in terms of the residues of the function 1/(1 - g). Under the assumption that g can be extended into a meromorphic function on the complex plane and some technical conditions, we obtain even an exact expansion of the renewal function. An...
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作者：Bluemmel, Tilmann; Rheinlaender, Thorsten
作者单位：University of Vienna; Technische Universitat Wien
摘要：We construct a large trader model using tools from nonlinear stochastic integration theory and an impact function. It encompasses many well-known models from the literature. In particular, the model allows price changes to depend on the size as well as on the speed and timing of the large trader's transactions. Moreover, a volume impact limit order book can be studied in this framework. Relaxing a condition about existence of a universal martingale measure governing all resulting small trader ...
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作者：Mossel, Elchanan; Roch, Sebastien
作者单位：Massachusetts Institute of Technology (MIT); University of Wisconsin System; University of Wisconsin Madison
摘要：We consider the reconstruction of a phylogeny from multiple genes under the multispecies coalescent. We establish a connection with the sparse signal detection problem, where one seeks to distinguish between a distribution and a mixture of the distribution and a sparse signal. Using this connection, we derive an information-theoretic trade-off between the number of genes, m, needed for an accurate reconstruction and the sequence length, k, of the genes. Specifically, we show that to detect a b...
