The comparison theorem for generalized backward stochastic differential equations is discussed. Some topics related to equations of this type are also investigated.
This paper deals with nonlinear expectations. The author obtains a nonlinear gen- eralization of the well-known Kolmogorov’s consistent theorem and then use it to con- struct ?ltration-consistent nonlinear expectatio...This paper deals with nonlinear expectations. The author obtains a nonlinear gen- eralization of the well-known Kolmogorov’s consistent theorem and then use it to con- struct ?ltration-consistent nonlinear expectations via nonlinear Markov chains. Com- pared to the author’s previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probabil- ity measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations. The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.展开更多
Concepts of g-supersolution, g-manrtingale, g-supermartingale are introduced, which are related to BSDE with Brownian motion and Poisson point process. A strict comparison theorem, monotonic limit theorem related to t...Concepts of g-supersolution, g-manrtingale, g-supermartingale are introduced, which are related to BSDE with Brownian motion and Poisson point process. A strict comparison theorem, monotonic limit theorem related to this type of BSDE are also discussed. As an application of these results, a nonlinear Doob-Meyer decomposition theorem is obtained.展开更多
基金in Shandong University, supported by National Natural Science Foundation of China (No.79790130)China Financial Policy Research Center, Renmin University of China.
文摘The comparison theorem for generalized backward stochastic differential equations is discussed. Some topics related to equations of this type are also investigated.
基金Project supported by the National Natural Science Foundation of China(No.10131040).
文摘This paper deals with nonlinear expectations. The author obtains a nonlinear gen- eralization of the well-known Kolmogorov’s consistent theorem and then use it to con- struct ?ltration-consistent nonlinear expectations via nonlinear Markov chains. Com- pared to the author’s previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probabil- ity measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations. The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.
文摘Concepts of g-supersolution, g-manrtingale, g-supermartingale are introduced, which are related to BSDE with Brownian motion and Poisson point process. A strict comparison theorem, monotonic limit theorem related to this type of BSDE are also discussed. As an application of these results, a nonlinear Doob-Meyer decomposition theorem is obtained.
