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作者：Ohashi, Alberto
作者单位：Universidade Estadual de Campinas
摘要：In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. By using support arguments we prove that the resulting model is arbitrage free under proportional transaction costs in the same spirit of Guasoni [Math. Finance 16 (2006) 569-582]. In particular, we obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. The second part of this paper deals with consistency problems related to the fract...
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作者：Zucca, Cristina; Sacerdote, Laura
作者单位：University of Turin
摘要：The inverse first-passage problem for a Wiener process (W(t))(t >= 0) seeks to determine a function b : R(+) -> R such that tau = inf{t > 0 vertical bar W(t) >= b(t)} has a given law. In this paper two methods for approximating the unknown function b are presented. The errors of the two methods are studied. A set of examples illustrates the methods. Possible applications are enlighted.
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作者：Collamore, Jeffrey F.
作者单位：University of Copenhagen
摘要：We develop sharp large deviation asymptotics for the probability of ruin in a Markov-dependent stochastic economic environment and study the extremes for some related Markovian processes which arise in financial and insurance mathematics, related to perpetuities and the ARCH(I) and GARCH(1,1) time series models. Our results build upon work of Goldie [Ann. Appl. Probab. 1 (1991) 126-166], who has developed tail asymptotics applicable for independent sequences of random variables subject to a ra...
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作者：Goldenshluger, Alexander; Zeevi, Assaf
作者单位：University of Haifa; Columbia University
摘要：We consider the one-armed bandit problem of Woodroofe [J. Amer Statist. Assoc. 74 (1979) 799-806], which involves sequential sampling from two populations: one whose characteristics are known, and one which depends on an unknown parameter and incorporates a covariate. The goal is to maximize cumulative expected reward. We study this problem in a minimax setting, and develop rate-optimal polices that involve suitable modifications of the myopic rule. It is shown that the regret, as well as the ...
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作者：Durrett, Rick; Remenik, Daniel
作者单位：Cornell University
摘要：We investigate an interacting particle system inspired by the gypsy moth, whose populations grow until they become sufficiently dense so that an epidemic reduces them to a low level. We consider this process on a random 3-regular graph and on the d-dimensional lattice and torus, with d >= 2. On the finite graphs with global dispersal or with a dispersal radius that grows with the number of sites, we prove convergence to a dynamical system that is chaotic for some parameter values. We conjectur...
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作者：Wu, Wei Biao
作者单位：University of Chicago
摘要：For statistical inference of means of stationary processes, one needs to estimate their time-average variance constants (TAVC) or long-run variances. For a stationary process, its TAVC is the sum of all its covariances and it is a multiple of the spectral density at zero. The classical TAVC estimate which is based on batched means does not allow recursive updates and the required memory complexity is O(n). We propose a faster algorithm which recursively computes the TAVC, thus having memory co...
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作者：Gnedin, Alexander V.; Iksanov, Alexander M.; Negadajlov, Pavlo; Roesler, Uwe
作者单位：Utrecht University; University of Kiel
摘要：We consider an occupancy scheme in which balls are identified with n points sampled from the standard exponential distribution, while the role of boxes is played by the spacings induced by an independent random walk with positive and nonlattice steps. We discuss the asymptotic behavior of five quantities: the index K-n* of the last occupied box, the number K-n of occupied boxes, the number K-n,K-0 of empty boxes whose index is at most K-n*, the index W-n of the first empty box and the number o...
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作者：Collet, P.; Giardina, C.; Redig, F.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Institut Polytechnique de Paris; Ecole Polytechnique; Eindhoven University of Technology; Leiden University - Excl LUMC; Leiden University
摘要：We consider matching with shifts for Gibbsian sequences. We prove that the maximal overlap behaves as clog it, where c is explicitly identified in terms of the thermodynamic quantities (pressure) of the underlying potential. Our approach is based on the analysis of the first and second moment of the number of overlaps of a given size. We treat both the case of equal sequences (and nonzero shifts) and independent sequences.
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作者：Liu, Yuping; Ma, Jin
作者单位：University of Southern California
摘要：In this paper the utility optimization problem for a general insurance model is studied. The reserve process of the insurance company is described by a stochastic differential equation driven by a Brownian motion and a Poisson random measure, representing the randomness from the financial market and the insurance claims, respectively. The random safety loading and stochastic interest rates are allowed in the model so that the reserve process is non-Markovian in general. The insurance company c...
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作者：Pemantle, Robin
作者单位：University of Pennsylvania
摘要：Consider a binary tree, to the vertices of which are assigned independent Bernoulli random variables with mean p <= 1/2. How many of these Bernoullis one must look at in order to find a path of length n from the root which maximizes, up to a factor of 1 - epsilon, the sum of the Bernoullis along the path? In the case p = 1/2 (the critical value for nontriviality), it is shown to take Theta(epsilon(-1)n) steps. In the case p < 1/2, the number of steps is shown to be at least n exp(const epsilon...
