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作者：Nutz, Marcel; Zhang, Yuchong
作者单位：Columbia University; Columbia University; University of Toronto
摘要：Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For instance, an agent may care only about states where she is still alive at the time of stopping, or a company may condition on not being bankrupt. We observe that conditional optimization is time-inconsistent due to the dynamic change of the conditioning probabi...
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作者：Breit, Dominic; Feireisl, Eduard; Hofmanova, Martina
作者单位：Heriot Watt University; Czech Academy of Sciences; Institute of Mathematics of the Czech Academy of Sciences; University of Bielefeld
摘要：We analyze the Markov property of solutions to the compressible Navier-Stokes system perturbed by a general multiplicative stochastic forcing. We show the existence of an almost sure Markov selection to the associated martingale problem. Our proof is based on the abstract framework introduced in Flandoli and Romito (Probab. Theory Related Fields 40 (2008) 407-458). A major difficulty arises from the fact, different from the incompressible case, that the velocity field is not continuous in time...
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作者：Harris, Simon C.; Johnston, Samuel G. G.; Roberts, Matthew I.
作者单位：University of Auckland; University College Dublin; University of Bath
摘要：Take a continuous-time Galton-Watson tree. If the system survives until a large time T, then choose k particles uniformly from those alive. What does the ancestral tree drawn out by these k particles look like? Some special cases are known but we give a more complete answer. We concentrate on near-critical cases where the mean number of offspring is 1 + mu/T for some mu is an element of R, and show that a scaling limit exists as T -> infinity. Viewed backwards in time, the resulting coalescent...
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作者：Caye, Thomas; Herdegen, Martin; Muhle-Karbe, Johannes
作者单位：Dublin City University; University of Warwick; Imperial College London
摘要：We study portfolio choice with small nonlinear price impact on general market dynamics. Using probabilistic techniques and convex duality, we show that the asymptotic optimum can be described explicitly up to the solution of a nonlinear ODE, which identifies the optimal trading speed and the performance loss due to the trading friction. Previous asymptotic results for proportional and quadratic trading costs are obtained as limiting cases. As an illustration, we discuss how nonlinear trading c...
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作者：Baik, Jinho; Bothner, Thomas
作者单位：University of Michigan System; University of Michigan; University of London; King's College London
摘要：The real Ginibre ensemble consists of n x n real matrices X whose entries are i.i.d. standard normal random variables. In sharp contrast to the complex and quaternion Ginibre ensemble, real eigenvalues in the real Ginibre ensemble attain positive likelihood. In turn, the spectral radius R-n = max(1 <= j <= n) vertical bar z(j)(X)vertical bar of the eigenvalues z(j)(X) is an element of C of a real Ginibre matrix X follows a different limiting law (as n -> infinity) for z(j) (X) is an element of...
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作者：Fang, Wei; Giles, Michael B.
作者单位：University of Oxford
摘要：This paper proposes an adaptive timestep construction for an Euler-Maruyama approximation of SDEs with nonglobally Lipschitz drift. It is proved that if the timestep is bounded appropriately, then over a finite time interval the numerical approximation is stable, and the expected number of timesteps is finite. Furthermore, the order of strong convergence is the same as usual, that is, order 1/2 for SDEs with a nonuniform globally Lipschitz volatility, and order 1 for Langevin SDEs with unit vo...
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作者：Hermon, Jonathan; Ben Morris; Qin, Chuan; Sly, Allan
作者单位：University of Cambridge; University of California System; University of California Davis; Princeton University
摘要：Given an infinite connected regular graph G = (V, E), place at each vertex Poisson(lambda) walkers performing independent lazy simple random walks on G simultaneously. When two walkers visit the same vertex at the same time they are declared to be acquainted. We show that when G is vertex-transitive and amenable, for all lambda > 0 a.s. any pair of walkers will eventually have a path of acquaintances between them. In contrast, we show that when G is nonamenable (not necessarily transitive) the...
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作者：Bardenet, Remi; Hardy, Adrien
作者单位：Universite de Lille; Centrale Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Inria
摘要：We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical N-1/2, where N is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures involving determinantal point processes associated with multivariate orthogonal polynomials, and we obtain root mean square errors that decrease as N-(1+1/ d)/2, where d is the dimension of the ambient space. First, we prove a central limit theorem (CLT) for the lin...
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作者：Popier, Alexandre; Zhou, Chao
作者单位：Le Mans Universite; National University of Singapore
摘要：In this work, we investigate an optimal liquidation problem under Knightian uncertainty. We obtain the value function and an optimal control characterised by the solution of a second-order BSDE with monotone generator and with a singular terminal condition.
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作者：Bally, Vlad
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Inria
摘要：We deal with f(t)(dv), the solution of the homogeneous 2D Boltzmann equation without cutoff. The initial condition f(0)(dv) may be any probability distribution (except a Dirac mass). However, for sufficiently hard potentials, the semigroup has a regularization property (see Probab. Theory Related Fields 151 (2011) 659-704): f(t)(dv) = f(t)(v) dv for every t > 0. The aim of this paper is to give upper bounds for f(t)(v), the most significant one being of type f(t)(v) <= Ct(-eta)e(-vertical bar ...
