This work proposes a new exchangeability test for random sequence through martingale-based approach. Its main contributions include 1) an additive martingale which is more amenable designing tests by exploiting the Hoeffding-Azuma lemma and 2) different betting functions constructing martingale. By choosing underlying probability density function of p-values as function, it can be shown that, w...

We study the joint laws of a continuous, uniformly integrable martingale, its maximum, and its minimum. In particular, we give explicit martingale inequalities which provide upper and lower bounds on the joint exit probabilities of a martingale, given its terminal law. Moreover, by constructing explicit and novel solutions to the Skorokhod embedding problem, we show that these bounds are tight....

This paper investigates testing conditional independence between Y and Z given λθ(X) for some θ ∈ Θ ⊂ R, for a function λθ(·) known upto a parameter θ ∈ Θ. First, the paper proposes a new method of conditional martingale transforms under which tests are asymptotically pivotal and asymptotically unbiased against √ n-converging Pitman local alternatives. Second, the paper performs an analysis of ...

In a model independent discrete time financial market, we discuss the richness of the family of martingale measures in relation to different notions of Arbitrage, generated by a class S of significant sets, which we call Arbitrage de la classe S. The choice of S reflects into the intrinsic properties of the class of polar sets of martingale measures. In particular: for S = {Ω}, absence of Model...

Let L be a multidimensional Lévy process under P in its own filtration. The f-minimal martingale measure Qq is defined as that equivalent local martingale measure for E(L) which minimizes the f-divergence E [ (dQ/dP ) ] for fixed q ∈ (−∞, 0) ∪ (1,∞). We give necessary and sufficient conditions for the existence of Qq and an explicit formula for its density. For q = 2, we relate the sufficient c...

Introduction In a data streaming setting, data points are observed one by one. The concepts to be learned from the data points may change infinitely often as the data is streaming. We extend the idea of testing exchangeability online [2] to a martingale framework to detect concept changes in time-varying data streams [P1]. •Two martingale tests using: (i) martingale values (MT1) and (ii) the ma...

It is often important, in applications of stochastic calculus to financial modelling, to know whether a given local martingale is a martingale or a strict local martingale. We address this problem in the context of a time-homogenous diffusion process with a finite lower boundary, presented as the solution of a driftless stochastic differential equation. Our main theorem demonstrates that the qu...

The Spontaneous Symmetry breaking in Quantum Finance considers the martingale condition stock market as a vacuum state if we express financial equations Hamiltonian form. original analysis for this phenomena ignores completely kinetic terms neighborhood of minimal potential terms. This is correct most cases. However, when deal with Martingale condition, it comes out that can also behave and the...