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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.
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作者：Jentzen, Arnulf; Kloeden, Peter; Winkel, Georg
作者单位：Princeton University; Goethe University Frankfurt
摘要：Recently, in a paper by Jentzen and Kloeden [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 649-667], a new method for simulating nearly linear stochastic partial differential equations (SPDEs) with additive noise has been introduced. The key idea was to use suitable linear functionals of the noise process in the numerical scheme which allow a higher approximation order to be obtained. Following this approach, a new simplified version of the scheme in the above named reference is ...
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作者：Guo, Xianping; Song, Xinyuan
作者单位：Sun Yat Sen University; Chinese University of Hong Kong
摘要：This paper is devoted to studying constrained continuous-time Markov decision processes (MDPs) in the class of randomized policies depending on state histories. The transition rates may be unbounded, the reward and costs are admitted to be unbounded from above and from below, and the state and action spaces are Polish spaces. The optimality criterion to be maximized is the expected discounted rewards, and the constraints can be imposed on the expected discounted costs. First, we give condition...
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作者：Hu, Yaozhong; Nualart, David; Song, Xiaoming
作者单位：University of Kansas
摘要：In this paper we study backward stochastic differential equations with general terminal value and general random generator. In particular, we do not require the terminal value be given by a forward diffusion equation. The randomness of the generator does not need to be from a forward equation, either. Motivated from applications to numerical simulations, first we obtain the L(p)-Holder continuity of the solution. Then we construct several numerical approximation schemes for backward stochastic...
