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作者：Marshall, Nicholas F.
作者单位：Yale University
摘要：Suppose f : [0, 1](2) -> R is a (c, alpha)-mixed Holder function that we sample at l points X-1,..., X-l chosen uniformly at random from the unit square. Let the location of these points and the function values f(X-1),..., f(X-l) be given. If l >= c(1)n log(2)n, then we can compute an approximation (f) over tilde such that parallel to integral -(integral) over tilde parallel to L-2 = O(n(-alpha) log(3/2)n), with probability at least 1- n(2-c1), where the implicit constant only depends on the c...
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作者：Cox, Alexander M. G.; Kinsley, Sam M.
作者单位：University of Bath
摘要：A leveraged exchange traded fund (LETF) is an exchange traded fund that uses financial derivatives to amplify the price changes of a basket of goods. In this paper, we consider the robust hedging of European options on a LETF, finding model-free bounds on the price of these options. To obtain an upper bound, we establish a new optimal solution to the Skorokhod embedding problem (SEP) using methods introduced in Beiglbock- Cox-Huesmann. This stopping time can be represented as the hitting time ...
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作者：Gu, Yu; Tsai, Li-Cheng
作者单位：Carnegie Mellon University; Columbia University
摘要：For the heat equation driven by a smooth, Gaussian random potential: partial derivative(t)u(epsilon) = 1/2 Delta u epsilon + u(epsilon) (xi(epsilon) - c(epsilon)), t > 0, chi is an element of R, where xi(e) converges to a spacetime white noise, and c(epsilon) is a diverging constant chosen properly, we prove that u(epsilon) converges in L-n to the solution of the stochastic heat equation for any n >= 1. Our proof is probabilistic, hence provides another perspective of the general result of Hai...
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作者：Hefter, Mario; Herzwurm, Andre; Mueller-Gronbach, Thomas
作者单位：Austrian Academy of Sciences; University of Kaiserslautern; University of Passau
摘要：We study pathwise approximation of scalar stochastic differential equations at a single time point or globally in time by means of methods that are based on finitely many observations of the driving Brownian motion. We prove lower error bounds in terms of the average number of evaluations of the driving Brownian motion that hold for every such method under rather mild assumptions on the coefficients of the equation. The underlying simple idea of our analysis is as follows: the lower error boun...
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作者：Viens, Frederi; Zhang, Jianfeng
作者单位：Michigan State University; University of Southern California
摘要：In this paper, we study dynamic backward problems, with the computation of conditional expectations as a special objective, in a framework where the (forward) state process satisfies a Volterra type SDE, with fractional Brownian motion as a typical example. Such processes are neither Markov processes nor semimartingales, and most notably, they feature a certain time inconsistency which makes any direct application of Markovian ideas, such as flow properties, impossible without passing to a pat...
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作者：Braunsteins, Peter; Hautphenne, Sophie
作者单位：University of Melbourne; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We consider a class of branching processes with countably many types which we refer to as Lower Hessenberg branching processes. These are multitype Galton-Watson processes with typeset X = {0, 1, 2,...}, in which individuals of type i may give birth to offspring of type j <= i + 1 only. For this class of processes, we study the set S of fixed points of the progeny generating function. In particular, we highlight the existence of a continuum of fixed points whose minimum is the global extinctio...
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作者：Huo, Ran; Durrett, Rick
作者单位：Duke University
摘要：Inspired by the spread of discontent as in the 2016 presidential election, we consider a voter model in which 0's are ordinary voters and 1's are zealots. Thinking of a social network, but desiring the simplicity of an infinite object that can have a nontrivial stationary distribution, space is represented by a tree. The dynamics are a variant of the biased voter: if x has degree d(x) then at rate d(x)p(k) the individual at x consults k >= 1 neighbors. If at least one neighbor is 1, they adopt...
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作者：Reinert, Gesine; Ross, Nathan
作者单位：University of Oxford; University of Melbourne
摘要：We provide a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for the Glauber dynamics of one of the sequences, and a simple expectation of the other. The result is applied to estimate, with explicit error, expectations of functions of random vectors for some Ising models and exponential random graphs in high temperature regimes.
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作者：Cruise, James R.; Wade, Andrew R.
作者单位：Heriot Watt University; Durham University
摘要：Each site of Z hosts a queue with arrival rate lambda. A single server, starting at the origin, serves its current queue at rate mu until that queue is empty, and then moves to the longest neighbouring queue. In the critical case lambda = mu, we show that the server returns to every site infinitely often. We also give a sharp iterated logarithm result for the server's position. Important ingredients in the proofs are that the times between successive queues being emptied exhibit doubly exponen...
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作者：Bayraktar, Erhan; Cvitanic, Jaksa; Zhang, Yuchong
作者单位：University of Michigan System; University of Michigan; California Institute of Technology; University of Toronto
摘要：We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank dependent, the equilibrium has a surprisingly explicit characterization, which allows us to conduct comparative statics and obtain explicit solution to several optimal reward design problems. In the general case when the players are heterogenous and payoffs are n...
