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作者：De Angelis, Tiziano; Ekstrom, Erik
作者单位：University of Leeds; Uppsala University
摘要：We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod reflection of the fund's value at a time-dependent optimal boundary. Our results are obtained by establishing for the first time a new connection between singular control problems with an absorbing boundary and optimal stopping problems on a diffusion reflected at 0...
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作者：Lux, Thibaut; Papapantoleon, Antonis
作者单位：Technical University of Berlin
摘要：We derive upper and lower bounds on the expectation of f (S) under dependence uncertainty, that is, when the marginal distributions of the random vector S = (S-1,..., S-d) are known but their dependence structure is partially unknown. We solve the problem by providing improved Frechet-Hoeffding bounds on the copula of S that account for additional information. In particular, we derive bounds when the values of the copula are given on a compact subset of [0, 1](d), the value of a functional of ...
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作者：Pistorius, Martijn; Stadje, Mitja
作者单位：Imperial College London; Ulm University
摘要：In this paper, we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency, we require that a dynamic deviation measures satisfies a generalised conditional variance formula. We show that, under a domination condition, dynamic deviation measures are characterised as the solutions to a certain class of stochastic differential equations. We establish for any dynamic deviation measure an integr...
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作者：Bovier, Anton; Hartung, Lisa
作者单位：University of Bonn; New York University; University of Bonn
摘要：We extend the results of Arguin et al. [Probab. Theory Related Fields 157 (2013) 535-574] and Aidekon et al. [Probab. Theory Related Fields 157 (2013) 405-451] on the convergence of the extremal process of branching Brownian motion by adding an extra dimension that encodes the location of the particle in the underlying Galton-Watson tree. We show that the limit is a cluster point process on R+ x R where each cluster is the atom of a Poisson point process on R+ x R with a random intensity measu...
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作者：Gaunt, Robert E.; Pickett, Alastair M.; Reinert, Gesine
作者单位：University of Oxford
摘要：This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein equation are obtained. These bounds involve both the shape parameter and the order of the derivative. Subsequently, Stein's method for chi-square approximation is applied to bound the distributional distance between Pearson's statistic and its limiting chi-square distribution, measured using smooth te...
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作者：Birkner, Matthias; Sun, Rongfeng
作者单位：Johannes Gutenberg University of Mainz; National University of Singapore
摘要：We consider a system of independent one-dimensional random walkers where new particles are added at the origin at fixed rate whenever there is no older particle present at the origin. A Poisson ansatz leads to a semi-linear lattice heat equation and predicts that starting from the empty configuration the total number of particles grows as c root t logt. We confirm this prediction and also describe the asymptotic macroscopic profile of the particle configuration.
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作者：Goncalves, Patricia; Landim, Claudio; Milanes, Aniura
作者单位：Universidade de Lisboa; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidade Federal de Minas Gerais
摘要：We consider one-dimensional, boundary driven, weakly asymmetric exclusion processes in contact with reservoirs at fixed density. For a general set of initial measures and by using a microscopic Cole-Hopf transformation, we derive the nonequilibrium fluctuations which are given by a generalized Ornstein-Uhlenbeck process.
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作者：Acciaio, Beatrice; Larsson, Martin
作者单位：University of London; London School Economics & Political Science; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider a continuous-time financial market that consists of securities available for dynamic trading, and securities only available for static trading. We work in a robust framework where a set of non-dominated models is given. The concept of semi-static completeness is introduced: it corresponds to having exact replication by means of semi-static strategies. We show that semi-static completeness is equivalent to an extremality property, and give a characterization of the induced filtratio...
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作者：Bayraktar, Erhan; Ya, Song
作者单位：University of Michigan System; University of Michigan; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We analyze a robust version of the Dynkin game over a set P of mutually singular probabilities. We first prove that conservative player's lower and upper value coincide (let us denote the value by V). Such a result connects' the robust Dynkin game with second-order doubly reflected backward stochastic differential equations. Also, we show that the value process V is a submartingale under an appropriately defined nonlinear expectation E up to the first time tau* when V meets the lower payoff pr...
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作者：Jenkins, Paul A.; Spano, Dario
作者单位：University of Warwick; University of Warwick
摘要：The Wright-Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this article, we demonstrate that it is in fact possible to simulate exactly from a broad class of Wright-Fisher diffusion processes and their bridges. For those diffusions corresponding to reversible, neutral evolution, our key idea is to exploit an eigenfunction expansion of the transition...
