Proof. The stochastic differential equation (2) follows directly from the (multivariate) Itô theorem, using the fact that Zt has the form Zt = u(Mt , [M ]t ). Every Itô integral process V ·M is a local martingale provided that M is a local martingale and V 2 L§(M), so for each n <1 the stopped process Z øn is a local martingale, where øn is the first time t such that [M ]t = n, and so it follow...

A supermartingale deflator (resp. local martingale deflator) multiplicatively transforms nonnegative wealth processes into supermartingales (resp. local martingales). A supermartingale numéraire (resp. local martingale numéraire) is a wealth process whose reciprocal is a supermartingale deflator (resp. local martingale deflator). It has been established in previous works that absence of arbitra...

This note studies the martingale property of a nonnegative, continuous local martingale Z, given as a nonanticipative functional of a solution to a stochastic differential equation. The condition states that Z is a (uniformly integrable) martingale if and only if an integral test of a related functional holds.

We derive a martingale representation for a contingent claim under a Markov-modulated version of the Black-Scholes economy. The martingale representation for the price of the claim is established with respect to an equivalent martingale measure chosen by the Esscher transform. Under some differentiability conditions for the coefficients of the price processes, we shall identify explicitly the i...

The existence of martingale selectors for a multivalued supermartin-gale with continuous parameter is proved.We also prove the weak regularity of multivalued supermartingales.Using the regularity of Banach-valued martingales,we show a multivalued supermartingale has a cadlag modiication under Kuratowski convergence. x1. Introduction Multivalued martingales and supermartingales with discrete par...

Traditional autocorrelation and variance ratio tests are based on serial uncorrelatedness rather than martingale difference. As such, they do not capture potential nonlinearity-in-mean behavior, which could lead to misleading inferences in favor of the martingale hypothesis. This paper employs various parametric and nonparametric nonlinear models as well as several model comparison criteria to ...

Abstract. We show that for a quantum L-martingale (X(t)), p > 2, there exists a Doob-Meyer decomposition of the submartingale (|X(t)|). A noncommutative counterpart of a classical process continuous with probability one is introduced, and a quantum stochastic integral of such a process with respect to an L-martingale, p > 2, is constructed. Using this construction, the uniqueness of the Doob-Me...

This paper introduces a dual way to price American options, based on simulating the paths of the option payoff, and of a judiciously chosen Lagrangian martingale. Taking the pathwise maximum of the payoff less the martingale provides an upper bound for the price of the option, and this bound is sharp for the optimal choice of Lagrangian martingale. As a first exploration of this method, four ex...

The martingale framework for detecting changes in data stream, currently only applicable to labeled data, is extended here to unlabeled data using clustering concept. The one-pass incremental changedetection algorithm (i) does not require a sliding window on the data stream, (ii) does not require monitoring the performance of the clustering algorithm as data points are streaming, and (iii) work...

We consider the problem of finding a real valued martingale fitting specified marginal distributions. For this to be possible, the marginals must be increasing in the convex order and have constant mean. We show that, under the extra condition that they are weakly continuous, the marginals can always be fitted in a unique way by a martingale which lies in a particular class of strong Markov pro...