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作者：Assing, Sigurd; Jacka, Saul; Ocejo, Adriana
作者单位：University of Warwick
摘要：We consider a pair (X, Y) of stochastic processes satisfying the equation dX = a(X)Y dB driven by a Brownian motion and study the monotonicity and continuity in y of the value function nu(x, y) = sup(tau) E-x,E-y[e(-q tau)g(X-tau)], where the supremum is taken over stopping times with respect to the filtration generated by (X, Y). Our results can successfully be applied to pricing American options where X is the discounted price of an asset while Y is given by a stochastic volatility model suc...
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作者：Gobet, Emmanuel; Landon, Nicolas
作者单位：Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Engie
摘要：In this work, we study the optimal discretization error of stochastic integrals, in the context of the hedging error in a multidimensional Ito model when the discrete rebalancing dates are stopping times. We investigate the convergence, in an almost sure sense, of the renormalized quadratic variation of the hedging error, for which we exhibit an asymptotic lower bound for a large class of stopping time strategies. Moreover, we make explicit a strategy which asymptotically attains this lower bo...
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作者：Rider, Brian; Sinclair, Christopher D.
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; University of Oregon
摘要：The real Ginibre ensemble refers to the family of n x n matrices in which each entry is an independent Gaussian random variable of mean zero and variance one. Our main result is that the appropriately scaled spectral radius converges in law to a Gumbel distribution as n -> infinity. This fact has been known to hold in the complex and quaternion analogues of the ensemble for some time, with simpler proofs. Along the way we establish a new form for the limit law of the largest real eigenvalue.
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作者：Giles, Michael B.; Szpruch, Lukasz
作者单位：University of Oxford
摘要：In this paper we introduce a new multilevel Monte Carlo (MLMC) estimator for multi-dimensional SDEs driven by Brownian motions. Giles has previously shown that if we combine a numerical approximation with strong order of convergence O(Delta t) with MLMC we can reduce the computational complexity to estimate expected values of functionals of SDE solutions with a root-mean-square error of epsilon from O(epsilon(-3)) to O(epsilon(-2)). However, in general, to obtain a rate of strong convergence h...
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作者：Beskos, Alexandros; Crisan, Dan; Jasra, Ajay
作者单位：National University of Singapore; University of London; University College London; Imperial College London
摘要：We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a target distribution on R-d for large d. It is well known [Bengtsson, Bickel and Li, In Probability and Statistics: Essays in Honor of David A. Freedman, D. Nolan and T. Speed, eds. (2008) 316-334 IMS; see also Pushing the Limits of Contemporary Statistics (2008) 318-329 IMS, Mon. Weather Rev. (2009) 136 (2009) 4629-4640] that using a single importance sampling step, one produces an a...
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作者：Arguin, Louis-Pierre; Zindy, Olivier
作者单位：Universite de Montreal; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite
摘要：We study the statistics of the extremes of a discrete Gaussian field with logarithmic correlations at the level of the Gibbs measure. The model is defined on the periodic interval [0, 1], and its correlation structure is nonhierarchical. It is based on a model introduced by Bacry and Muzy [Comm. Math. Phys. 236 (2003) 449-475] (see also Barral and Mandelbrot [Probab. Theory Related Fields 124 (2002) 409-430]), and is similar to the logarithmic Random Energy Model studied by Carpentier and Le D...
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作者：Pal, Soumik d; Shkolnikov, Mykhaylo
作者单位：University of Washington; University of Washington Seattle; University of California System; University of California Berkeley
摘要：We consider a finite or countable collection of one-dimensional Brownian particles whose dynamics at any point in time is determined by their rank in the entire particle system. Using transportation cost inequalities for stochastic processes we provide uniform fluctuation bounds for the ordered particles, their local time of collisions and various associated statistics over intervals of time. For example, such processes, when exponentiated and rescaled, exhibit power law decay under stationari...
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作者：Larsson, Martin
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Finance Institute (SFI)
摘要：When a strict local martingale is projected onto a subfiltration to which it is not adapted, the local martingale property may be lost, and the finite variation part of the projection may have singular paths. This phenomenon has consequences for arbitrage theory in mathematical finance. In this paper it is shown that the loss of the local martingale property is related to a measure extension problem for the associated Follmer measure. When a solution exists, the finite variation part of the pr...
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作者：Hegarty, Peter; Martinsson, Anders
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：We present rigorous mathematical analyses of a number of well-known mathematical models for genetic mutations. In these models, the genome is represented by a vertex of the n-dimensional binary hypercube, for some n, a mutation involves the flipping of a single bit, and each vertex is assigned a real number, called its fitness, according to some rules. Our main concern is with the issue of existence of (selectively) accessible paths; that is, monotonic paths in the hypercube along which fitnes...
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作者：Kang, Weining; Ramanan, Kavita
作者单位：University System of Maryland; University of Maryland Baltimore; Brown University
摘要：Given a domain G, a reflection vector field d(center dot) on partial derivative G, the boundary of G; and drift and dispersion coefficients b(center dot) and sigma(center dot), let L be the usual second-order elliptic operator associated with b(center dot) and sigma(center dot). Under mild assumptions on-the coefficients and reflection vector field, it is shown that when the associated submartingale problem is well posed, a probability measure pi on (G) over bar with pi (partial derivative G) ...
