奇异Hamilton-Jacobi-Bellman方程粘性解的存在唯一性  

EXISTENCE AND UNIQUENESS OF THE VISCOSITY SOLUTION TO SOME SINGULAR HJB EQUATIONS

作　　者：王子亭[1] 梁月[1] 王晓洁[1] 

机构地区：[1]中国石油大学(华东)数学与计算科学学院,青岛266555

出　　处：《系统科学与数学》2011年第8期1000-1009,共10页Journal of Systems Science and Mathematical Sciences

基　　金：中央高校基本科研业务费专项资金资助课题(09Cx04020A)

摘　　要：研究系数在边界点有奇性的一类Hamilton-Jacobi-Bellman(HJB)方程的粘性解的存在唯一性问题及解的渐近估计,这类问题包括波动系数振荡或爆破的情况.奇异HJB方程在随机最优控制和金融数学等许多领域都有重要的应用,包括金融数学中的随机利率模型.应用粘性上下解理论建立了一类奇异HJB方程的比较原理,给出了粘性解存在唯一性的条件.This paper is considered with the existence and uniqueness of the viscosity solution to some Hamilton-Jacobi-Bellman （HJB） equations with singular coefficients near at the boundary with either vanishing, or oscillating, or blowing-up diffusion coefficients. The singular HJB equation has been applied to stochastic optimal control and financial mathematics, including stochastic rate CIR model. By means of viscosity super-solution and viscosity sub- solution theory, the comparison principle of viscosity solution to the singular HJB equation is obtained, and the conditions of the existence and uniqueness of the solution are given.

关 键 词：奇异HJB方程 粘性解 随机利率 CIR模型 爆破 

分 类 号：O175[理学—数学]