Martingale representation theorem for theG-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 Martingale Decomposition Theorem

A Martingale System Theorem for Stock Investments

In tlus paper we consider an investment strategy called dollar-cast-averaging (DCA). It is well known that the argument in favor of DCA is flawed: an investor cannot get something for nothing. Probabilists have made tltis type of flaw precise with theorems like the optional sampling theorem or, more generally, the martingale system theorem (see e.g. [4]). It is interesting that the usual martin...

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 Central Limit Theorem

We present a proof of a martingale central limit theorem (Theorem 2) due to McLeish (1974). Then, an application to Markov chains is given.