Bibliographic Details
| Title: |
NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS. |
| Authors: |
Peng Shige1 peng@sdu.edu.cn |
| Superior Title: |
Chinese Annals of Mathematics. Apr2005, Vol. 26 Issue 2, p159-184. 26p. |
| Subject Terms: |
*MARKOV processes, *STOCHASTIC processes, *DIFFERENTIAL equations, *MARTINGALES (Mathematics), *MATHEMATICS |
| Abstract: |
This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov's consistent theorem and then use it to construct filtration-consistent nonlinear expectations via nonlinear Markov chains. Compared 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 probability 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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Academic Search Premier |