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| NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS |
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Citation： |
PENG Shige.NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS[J].Chinese Annals of Mathematics B,2005,26(2):159~184 |
| Page view： 2723
Net amount： 957 |
Authors： |
PENG Shige; |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10131040). |
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| 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 $L^p$-norms and
$L^\infty$-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. |
Keywords： |
Backward stochastic differential equations, Nonlinear expectation, Nonlinear
expected utilities, Measure of risk, g-expectation, Nonlinear Markov
chain, g-martingale, Nonlinear martingale, Nonlinear Kolmogorov’s
consistent theorem, Doob-Meyer decomposition |
Classification： |
60H10 |
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