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作者：Kharroubi, Idris; Langrene, Nicolas; Huyen Pham
作者单位：Universite PSL; Universite Paris-Dauphine; Universite Paris Cite
摘要：We propose a new probabilistic numerical scheme for fully nonlinear equation of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem, which is based on the Feynman Kac representation in [Kharroubi and Pham (2014)] by means of control randomization and backward stochastic differential equation with nonpositive jumps. We study a discrete time approximation for the minimal solution to this class of BSDE when the time step goes to zero, which provides both an approximation f...
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作者：Ferrari, Patrik L.; Spohn, Herbert; Weiss, Thomas
作者单位：University of Bonn
摘要：We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a SchUtz-type formula is derived for the transition probability. We investigate an infinite system with periodic initial configuration, that is, particles are located at the integer lattice at time zero. The joint distribution of the positions of a finite subset of particles is expressed as a Fredholm determinant with a kernel defining a signe...
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作者：Keller-Ressel, Martin; Mayerhofer, Eberhard
作者单位：Technical University of Berlin; Dublin City University
摘要：We investigate the maximal domain of the moment generating function of affine processes in the sense of Duffle, Filipovie and Schachermayer [Ann. AppL Probab. 13 (2003) 984-1053], and we show the validity of the affine transform formula that connects exponential moments with the solution of a generalized Riccati differential equation. Our result extends and unifies those preceding it (e.g., Glasserman and Kim [Math. Finance 20 (2010) 1-33], Filipovie and Mayerhofer [Radon Ser. Comput. Appl. Ma...
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作者：Bertoin, Jean; Uribe Bravo, Geronimo
作者单位：University of Zurich; Universidad Nacional Autonoma de Mexico
摘要：We consider Bernoulli bond percolation on a large scale-free tree in the supercritical regime, meaning informally that there exists a giant cluster with high probability. We obtain a weak limit theorem for the sizes of the next largest clusters, extending a recent result in Bertoin [Random Structures Algorithms 44 (2014) 29-44] for large random recursive trees. The approach relies on the analysis of the asymptotic behavior of branching processes subject to rare neutral mutations, which may be ...
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作者：Le, Huiling
作者单位：University of Nottingham
摘要：This paper studies rescaled images, under exp(mu)(-1) of the sample Frechet means of i.i.d. random variables {X-k vertical bar k >= 1} with Frechet mean mu on a Riemannian manifold. We show that, with appropriate scaling, these images converge weakly to a diffusion process. Similar to the Euclidean case, this limiting diffusion is a Brownian motion up to a linear transformation. However, in addition to the covariance structure of exp(mu)(-1) (X-1), this linear transformation also depends on th...
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作者：Bouchard, Bruno; Nutz, Marcel
作者单位：Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris; Columbia University
摘要：We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of martingale measures. In the arbitrage-free case, we show that optimal superhedging strategies exist for general contingent claims, and that the minimal superhedging price is given by the supremum...
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作者：Fournier, Nicolas
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：We consider the 3D spatially homogeneous Boltzmann equation for (true) hard and moderately soft potentials. We assume that the initial condition is a probability measure with finite energy and is not a Dirac mass. For hard potentials, we prove that any reasonable weak solution immediately belongs to some Besov space. For moderately soft potentials, we assume additionally that the initial condition has a moment of sufficiently high order (8 is enough) and prove the existence of a solution that ...
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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...
