Martingale Representation Theorem for the G-Expectation

Martingale Representation Theorem for the G-expectation

This paper considers the nonlinear theory of G-martingales as introduced by Peng in [16, 17]. A martingale representation theorem for this theory is proved by using the techniques and the results established in [20] for the second order stochastic target problems and the second order backward stochastic differential equations. In particular, this representation provides a hedging strategy in a ...

A complete representation theorem for G-martingales

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The Martingale Central Limit Theorem

One of the most useful generalizations of the central limit theorem is the martingale central limit theorem of Paul Lévy. Lévy was in part inspired by Lindeberg’s treatment of the central limit theorem for sums of independent – but not necessarily identically distributed – random variables. Lindeberg formulated what, in retrospect, is the right hypothesis, now known as the Lindeberg condition,1...

A Martingale Decomposition Theorem

An integral representation theorem of g-expectations

There are two classes of nonlinear expectations, one is the Choquet expectation given by Choquet (1955), the other is the Peng’s g-expectation given by Peng (1997) via backward differential equations (BSDE). Recently, Peng raised the following question: can a g-expectation be represented by a Choquet expectation? In this paper, we provide a necessary and sufficient condition on g-expectations u...