A Martingale Decomposition Theorem

A Martingale Decomposition Theorem

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.

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...

An Explicit Martingale Version of Brenier’s Theorem

By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in [3, 24]. In this paper, we extend the one-dimensional Brenier’s theorem to the present martingale version. We provide the explicit martingale optimal transference plans for a remarkable class of coupling functions correspon...