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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：Mendoza-Arriaga, Rafael; Linetsky, Vadim
作者单位：University of Texas System; University of Texas Austin; Northwestern University
摘要：The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process (X, D) of a diffusion state variable X driving default intensity and a default indicator process D and time change it with a Levy subordinator T. We characterize the time-changed process (X-t(phi), D-t(phi)) = (X (T-t), D (T-t)) as a Markovian Ito semimartingale and show from the Doob-Meyer decompositi...
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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：Faure, Mathieu; Schreiber, Sebastian J.
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite; University of California System; University of California Davis
摘要：We analyze quasi-stationary distributions {mu(epsilon)}(epsilon>0) of a family of Markov chains {X-epsilon}(epsilon>0) that are random perturbations of a bounded, continuous map F : M -> M, where M is a closed subset of R-k. Consistent with many models in biology, these Markov chains have a closed absorbing set M-0 subset of M such that F(M-0) = M-0 and F (M \ M-0) = M \ M-0. Under some large deviations assumptions on the random perturbations, we show that, if there exists a positive attractor...
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作者：Jahnel, Benedikt; Kuelske, Christof
作者单位：Ruhr University Bochum
摘要：We consider a class of discrete q-state spin models defined in terms of a translation-invariant quasilocal specification with discrete clock-rotation invariance which have extremal Gibbs measures mu(1)(phi) labeled by the uncountably many values of phi in the one-dimensional sphere (introduced by van Enter, Opoku, Kulske [J. Phys. A 44 (2011) 475002, 11]). In the present paper we construct an associated Markov jump process with quasilocal rates whose semigroup (S-t)(t >= 0) acts by a continuou...
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作者：Bayer, Christian; Schoenmakers, John
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced in Milstein, Schoenmakers and Spokoiny [Bernoulli 10 (2004) 281-312] in the context of a forward-reverse tr...
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作者：Lucon, Eric; Stannat, Wilhelm
作者单位：Technical University of Berlin
摘要：Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in R-m in the presence of a random environment and with spatial extension: each diffusion is attached to one site of the lattice Z(d), and the interaction between two diffusions is attenuated by a spatial weight that depends on their positions. For a general class of singular weights (including the case already considered ...
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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：Berestycki, Julien; Berestycki, Nathanael; Limic, Vlada
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We describe a new general connection between Lambda-coalescents and genealogies of continuous-state branching processes. This connection is based on the construction of an explicit coupling using a particle representation inspired by the lookdown process of Donnelly and Kurtz. This coupling has the property that the coalescent comes down from infinity if and only if the branching process becomes extinct, thereby answering a question of Bertoin and Le Gall. The coupling also offers new perspect...
