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作者：Neal, Peter; Roberts, Gareth; Yuen, Wai Kong
作者单位：University of Manchester; University of Warwick; Brock University
摘要：We consider the optimal scaling problem for high-dimensional random walk Metropolis (RWM) algorithms where the target distribution has a discontinuous probability density function. Almost all previous analysis has focused upon continuous target densities. The main result is a weak convergence result as the dimensionality d of the target densities converges to infinity. In particular, when the proposal variance is scaled by d(-2), the sequence of stochastic processes formed by the first compone...
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作者：Bayraktar, Erhan; Huang, Yu-Jui; Song, Qingshuo
作者单位：University of Michigan System; University of Michigan; City University of Hong Kong
摘要：Our goal is to resolve a problem proposed by Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain probability, as a function of the market configuration and time to maturity. We show that this value function is the smallest nonnegative viscosity supersolution of a nonlinear PDE. As in Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.], we do n...
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作者：Cisse, Mamadou; Patie, Pierre; Tanre, Etienne
作者单位：Universite Libre de Bruxelles; Universite Cote d'Azur
摘要：In this paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results to the class of one-sided regular Feller processes. This generalizes the result of Beibel and Lerche [Statist. Sinica 7 (1997) 93-108] and [Tear. Veroyatn. Primen. 45 (2000) 657-669] and Irles and Paulsen [Sequential Anal. 23 (2004) 297-316]. Our approach relies on a combination of techniques borrow...
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作者：Ekstrom, Erik; Tysk, Johan
作者单位：Uppsala University
摘要：We study the term structure equation for single-factor models that predict nonnegative short rates. In particular, we show that the price of a bond or a bond option is the unique classical solution to a parabolic differential equation with a certain boundary behavior for vanishing values of the short rate. If the boundary is attainable then this boundary behavior serves as a boundary condition and guarantees uniqueness of solutions. On the other hand, if the boundary is nonattainable then the ...
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作者：Gerhold, Stefan
作者单位：Technische Universitat Wien
摘要：We investigate the Longstaff-Schwartz algorithm for American option pricing assuming that both the number of regressors and the number of Monte Carlo paths tend to infinity. Our main results concern extensions, respectively, applications of results by Glasserman and Yu [Ann. Appl. Probab. 14 (2004) 2090-2119] and Stentoft [Manag. Sci. 50 (2004) 1193-1203] to several Levy models, in particular the geometric Meixner model. A convenient setting to analyze this convergence problem is provided by t...
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作者：Terasawa, Yutaka; Yoshida, Nobuo
作者单位：University of Tokyo; Kyoto University
摘要：We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here the extra stress tensor of the fluid is given by a polynomial of degree p - 1 of the rate of strain tensor, while the colored noise is considered as a random force. We investigate the existence and the uniqueness of weak solutions to this SPDE.
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作者：Kobylanski, Magdalena; Quenez, Marie-Claire; Rouy-Mironescu, Elisabeth
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We study the optimal multiple stopping time problem defined for each stopping time S by v(S) = ess sup(tau 1), ... , (tau d) (>=) (S) E[psi(tau(1), ... , tau(d))vertical bar F-S]. The key point is the construction of a new reward phi such that the value function v(S) also satisfies v(S) = ess sup(theta >= S) E[phi(theta)vertical bar F-S]. This new reward phi is not a right-continuous adapted process as in the classical case, but a family of random variables. For such a reward, we prove a new e...
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作者：Del Moral, Pierre; Rio, Emmanuel
作者单位：Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux; Universite Paris Saclay; Universite Paris Saclay
摘要：This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of nonlinear measure valued processes. We combine an original stochastic perturbation analysis with a concentration analysis for triangular arrays of conditionally independent random sequences, which may be of independent interest. Under some additional stability properties of the limiting measure valued processes, uniform concentrat...
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作者：Barndorff-Nielsen, Ole Eiler; Stelzer, Robert
作者单位：Aarhus University; Technical University of Munich; Technical University of Munich
摘要：Univariate superpositions of Ornstein-Uhlenbeck-type processes (OU), called supOU processes, provide a class of continuous time processes capable of exhibiting long memory behavior. This paper introduces multivariate supOU processes and gives conditions for their existence and finiteness of moments. Moreover, the second-order moment structure is explicitly calculated, and examples exhibit the possibility of long-range dependence. Our supOU processes are defined via homogeneous and factorizable...
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作者：Richou, Adrien
作者单位：Universite de Rennes
摘要：This article deals with the numerical resolution of Markovian backward stochastic differential equations (BSDEs) with drivers of quadratic growth with respect to z and bounded terminal conditions. We first show some bound estimates on the process Z and we specify the Zhang's path regularity theorem. Then we give a new time discretization scheme with a nonuniform time net for such BSDEs and we obtain an explicit convergence rate for this scheme.
