In this paper , we investigate comparison principle for semicontinuous viscosity solutions of fully nonlinear elliptic equation with nonlocal intergro - differential item . this kind of equation is from diffusion process with jumps and has important application in stochastic control and finance mathematics 本文研究一类带有非局部积分项的完全非线性椭圆型方程粘性解的比较原理,这类方程源自带跳跃的扩散过程,在随机控制,金融数学中有广泛而重要的应用。
This paper study the character and application of the solution of bsde , the main results include : for the second kind of bsde , the existence and uniqueness of the solution under non - lipschitz condition , comparison theorem and stability are established , under weaker condition , the existence of the minimal and maximal solution is proved and the application in stochastic control and utility function is given ; for the first kind of bsde , under weaker condition , the existence of minimal and maximal solution . stability , comparison theorem and application to utility function are proved 本文研究倒向随机微分方程解的性质及其应用,主要结果有:针对第二类方程,讨论了在非lipschitz条件下倒向随机微分方程解的存在唯一性,比较定理及稳定性等,在更弱条件下,得到了倒向随机微分方程的最大解和最小解的存在性,在此基础之上,给出了在随机控制及效用函数方面的应用;针对第一类方程,同样在较弱条件下,证明了方程最大、最小解的存在性、稳定性、比较定理及其在效用函数的应用。
Stochastic control or stochastic optimal control is a subfield of control theory which deals with the existence of uncertainty either in observations of the data or in the things that drive the evolution of the data. The designer assumes, in a Bayesian probability-driven fashion, that random noise with known probability distribution affects the evolution and observation of the state variables.