A Sufficient and Necessary Condition for G-Expectation to be Linear
- 10.2991/icemc-16.2016.77How to use a DOI?
- Backward stochastic differential equations; Peng’s g-expectation; Mathematical expectation; Lipschitz condition; Girsanov Theorem
In general, Peng’s g-expectation is a nonlinear mathematical expectation. However, if the function g(t, x, y) satisfies some properties, the g-expectation is expected to be linear. For g-expectation, we have the following conclusions: The necessary and sufficient condition for g- expectation to have linear properties is that the function g has nothing to do with variable y, and g is linear with variable z. In this case, there exists a probability measure Q, under which the linear expectation is equivalent to Peng’s g-expectation.
- © 2016, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - CONF AU - Qixia Zhang AU - Qiliang Sun PY - 2016/05 DA - 2016/05 TI - A Sufficient and Necessary Condition for G-Expectation to be Linear BT - Proceedings of the 2016 International Conference on Education, Management and Computer Science PB - Atlantis Press SP - 374 EP - 378 SN - 1951-6851 UR - https://doi.org/10.2991/icemc-16.2016.77 DO - 10.2991/icemc-16.2016.77 ID - Zhang2016/05 ER -