In this paper, a class of nonlinear stochastic partial differential equations with discontinuous coefficients is investigated. This study is motivated by some research on stochastic viscosity solutions under non-Lipsc...In this paper, a class of nonlinear stochastic partial differential equations with discontinuous coefficients is investigated. This study is motivated by some research on stochastic viscosity solutions under non-Lipschitz conditions recently. By studying the solutions of backward doubly stochastic differential equations with discontinuous coefficients and constructing a new approximation function f<sub>n</sub> to the coefficient f, we get the existence of stochastic viscosity sub-solutions (or super-solutions).The results of this paper can be seen as the extension and application of related articles.展开更多
In this paper,we prove an existence and uniqueness theorem for backward doubly stochastic differential equations under a new kind of stochastic non-Lipschitz condition which involves stochastic and timedependent condi...In this paper,we prove an existence and uniqueness theorem for backward doubly stochastic differential equations under a new kind of stochastic non-Lipschitz condition which involves stochastic and timedependent condition.As an application,we use the result to obtain the existence of stochastic viscosity solution for some nonlinear stochastic partial differential equations under stochastic non-Lipschitz conditions.展开更多
This paper addresses a finite difference approximation for an infinite dimensional Black-Scholesequation obtained by Chang and Youree (2007).The equation arises from a consideration ofan European option pricing proble...This paper addresses a finite difference approximation for an infinite dimensional Black-Scholesequation obtained by Chang and Youree (2007).The equation arises from a consideration ofan European option pricing problem in a market in which stock prices and the riskless asset prices havehereditary structures.Under a general condition on the payoff function of the option,it is shown thatthe pricing function is the unique viscosity solution of the infinite dimensional Black-Scholes equation.In addition,a finite difference approximation of the viscosity solution is provided and the convergenceresults are proved.展开更多
文摘In this paper, a class of nonlinear stochastic partial differential equations with discontinuous coefficients is investigated. This study is motivated by some research on stochastic viscosity solutions under non-Lipschitz conditions recently. By studying the solutions of backward doubly stochastic differential equations with discontinuous coefficients and constructing a new approximation function f<sub>n</sub> to the coefficient f, we get the existence of stochastic viscosity sub-solutions (or super-solutions).The results of this paper can be seen as the extension and application of related articles.
基金supported by Beijing Natural Science Foundation(No.1222004)Yuyou Project of North University of Technology(No.207051360020XN140/007)Scientific Research Foundation of North University of Technology(No.110051360002)。
文摘In this paper,we prove an existence and uniqueness theorem for backward doubly stochastic differential equations under a new kind of stochastic non-Lipschitz condition which involves stochastic and timedependent condition.As an application,we use the result to obtain the existence of stochastic viscosity solution for some nonlinear stochastic partial differential equations under stochastic non-Lipschitz conditions.
基金supported by a grant W911NF-04-D-0003 from the US Army Research Office
文摘This paper addresses a finite difference approximation for an infinite dimensional Black-Scholesequation obtained by Chang and Youree (2007).The equation arises from a consideration ofan European option pricing problem in a market in which stock prices and the riskless asset prices havehereditary structures.Under a general condition on the payoff function of the option,it is shown thatthe pricing function is the unique viscosity solution of the infinite dimensional Black-Scholes equation.In addition,a finite difference approximation of the viscosity solution is provided and the convergenceresults are proved.
