A Sufficient and Necessary Condition for G-Expectation to be Linear

DOI

10.2991/icemc-16.2016.77How to use a DOI?

Keywords

Backward stochastic differential equations; Peng’s g-expectation; Mathematical expectation; Lipschitz condition; Girsanov Theorem

Abstract

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.

Copyright

© 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/).

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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  -