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作者：Narayanan, Hariharan
作者单位：University of Washington; University of Washington Seattle; University of Washington; University of Washington Seattle
摘要：We present a Markov chain, Dikin walk, for sampling from a convex body equipped with a self-concordant barrier. This Markov chain corresponds to a natural random walk with respect to a Riemannian metric defined using the Hessian of the barrier function. For every convex set of dimension n, there exists a self-concordant barrier whose self-concordance parameter is O (n). Consequently, a rapidly mixing Markov chain of the kind we describe can be defined (but not always be efficiently implemented...
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作者：Dereich, Steffen; Li, Sangmeng
作者单位：University of Munster
摘要：In this article, we consider multilevel Monte Carlo for the numerical computation of expectations for stochastic differential equations driven by Levy processes. The underlying numerical schemes are based on jump adapted Euler schemes. We prove stable convergence of an idealised scheme. Further, we deduce limit theorems for certain classes of functionals depending on the whole trajectory of the process. In particular, we allow dependence on marginals, integral averages and the supremum of the ...
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作者：Henry-Labordere, Pierre; Obloj, Jan; Spoida, Peter; Touzi, Nizar
作者单位：University of Oxford; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：We obtain bounds on the distribution of the maximum of a martingale with fixed marginals at finitely many intermediate times. The bounds are sharp and attained by a solution to n-marginal Skorokhod embedding problem in Obloj and Spoida [An iterated Azema-Yor type embedding for finitely many marginals (2013) Preprint]. It follows that their embedding maximizes the maximum among all other embeddings. Our motivating problem is superhedging lookback options under volatility uncertainty for an inve...
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作者：Marinucci, Domenico; Vadlamani, Sreekar
作者单位：University of Rome Tor Vergata; Tata Institute of Fundamental Research (TIFR); TIFR Centre for Applicable Mathematics (CAM), Bengaluru
摘要：In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields. In particular, we consider both random spherical harmonics and their smoothed averages, which can be viewed as random wavelet coefficients in the continuous case. For such fields, we consider smoothed polynomial transforms; we focus on the geometry of their excursion sets, and we study their asymptotic behaviour, i...
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作者：Hug, Daniel; Last, Guenter; Schulte, Matthias
作者单位：Helmholtz Association; Karlsruhe Institute of Technology
摘要：Let Z be a Boolean model based on a stationary Poisson process it of compact, convex particles in Euclidean space R-d. Let W denote a compact, convex observation window. For a large class of functionals psi, formulas for mean values of psi(Z boolean AND W) are available in the literature. The first aim of the present work is to study the asymptotic covariances of general geometric (additive, translation invariant and locally bounded) functionals of Z boolean AND W for increasing observation wi...
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作者：Feng, Han; Hobson, David
作者单位：University of Warwick
摘要：This paper studies a variant of the contest model introduced in Seel and Strack [J. Econom. Theory 148 (2013) 2033-2048]. In the Seel-Strack contest, each agent or contestant privately observes a Brownian motion, absorbed at zero, and chooses when to stop it. The winner of the contest is the agent who stops at the highest value. The model assumes that all the processes start from a common value x(0) > 0 and the symmetric Nash equilibrium is for each agent to utilise a stopping rule which yield...
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作者：Hackmann, Daniel; Kuznetsov, Alexey
作者单位：York University - Canada
摘要：Levy processes with completely monotone jumps appear frequently in various applications of probability. For example, all popular stock price models based on Levy processes (such as the Variance Gamma, CGMY/KoBoL and Normal Inverse Gaussian) belong to this class. In this paper we continue the work started in [Int. J. Theor. Appl. Finance 13 (2010) 63-91, Quant. Finance 10 (2010) 629-644] and develop a simple yet very efficient method for approximating processes with completely monotone jumps by...
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作者：Chassagneux, Jean-Francois; Richou, Adrien
作者单位：Imperial College London; Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux; CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：This article deals with the numerical approximation of Markovian backward stochastic differential equations (BSDEs) with generators of quadratic growth with respect to z and bounded terminal conditions. We first study a slight modification of the classical dynamic programming equation arising from the time-discretization of BSDEs. By using a linearization argument and BMO martingales tools, we obtain a comparison theorem, a priori estimates and stability results for the solution of this scheme...
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作者：Duffy, James A.
作者单位：University of Oxford; University of Oxford
摘要：We provide a uniform law for the weak convergence of additive functionals of partial sum processes to the local times of linear fractional stable motions, in a setting sufficiently general for statistical applications. Our results are fundamental to the analysis of the global properties of nonparametric estimators of nonlinear statistical models that involve such processes as covariates.
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作者：Griffin, Philip S.
作者单位：Syracuse University
摘要：Recent studies have demonstrated an interesting connection between the asymptotic behavior at ruin of a Levy insurance risk process under the Cramer-Lundberg and convolution equivalent conditions. For example, the limiting distributions of the overshoot and the undershoot are strikingly similar in these two settings. This is somewhat surprising since the global sample path behavior of the process under these two conditions is quite different. Using tools from excursion theory and fluctuation t...
