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Hardy Martingales and the Unconditional Convergence of Martingales
Bulletin of the London Mathematical Society, 1991The class of Hardy martingales is introduced. These are martingales taking values in a complex Banach space whose increments, conditional on the past, are in the appropriate Hardy space. Such martingales are plurisubharmonic, and so every \(L^ 1\) bounded Hardy martingale which connverges in probability also converges in norm.
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2005
Martingale boosting is a simple and easily understood technique with a simple and easily understood analysis. A slight variant of the approach provably achieves optimal accuracy in the presence of random misclassification noise.
Philip M. Long, Rocco A. Servedio
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Martingale boosting is a simple and easily understood technique with a simple and easily understood analysis. A slight variant of the approach provably achieves optimal accuracy in the presence of random misclassification noise.
Philip M. Long, Rocco A. Servedio
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Quantitative Finance, 2005
We characterize strictly arbitrage-free markets of European options where only a discrete set of options is traded. We then construct martingales which reprice all given options and which are most expensive among all martingales with this property. We also present algorithms to adjust real life market data and to construct expensive martingales ...
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We characterize strictly arbitrage-free markets of European options where only a discrete set of options is traded. We then construct martingales which reprice all given options and which are most expensive among all martingales with this property. We also present algorithms to adjust real life market data and to construct expensive martingales ...
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Quantum Martingales that are Reverse Martingales are Multiples of the Identity
Bulletin of the London Mathematical Society, 1984Let \({\mathcal C}\) be a hyperfinite \(II_ 1\) factor, m the normal faithful central state (probability trace) on \({\mathcal C}\). For \(1\leq p\leq \infty\) define \(L^ p({\mathcal C})\) to be the completion of \({\mathcal C}\) with respect to the \(L^ p\)-norm \(\| u\|_ p=m(| u|^ p)^{1/p},\) \(u\in {\mathcal C}\).
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Operations Research, 1992
In establishing the seminal result PASTA (Poisson Arrivals See Time Averages), R. Wolff (1982) constructed a martingale, and demonstrated that PASTA was a consequence of a strong law of large numbers of this martingale. Here we establish a central limit theorem for the PASTA martingale, and characterize its asymptotic normality. The result can be used
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In establishing the seminal result PASTA (Poisson Arrivals See Time Averages), R. Wolff (1982) constructed a martingale, and demonstrated that PASTA was a consequence of a strong law of large numbers of this martingale. Here we establish a central limit theorem for the PASTA martingale, and characterize its asymptotic normality. The result can be used
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On martingales and feller semigroups
Results in Mathematics, 1992The author gives a clean characterization theorem which stems from the work of \textit{D. W. Stroock} and \textit{S. R. S. Varadhan} [Multidimensional diffusion processes (1979; Zbl 0426.60069)] on martingale problems in multidimensional diffusion. Let \(E^ \Delta\) be the one point compactification of the locally compact Hausdorff space \(E\).
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Martingales; reversed martingales and the Skorokhod embedding
1982Thesis (Ph.D.) -- La Trobe University, 1982.; Submitted to the Dept. of Mathematical Statistics, School of Physical Sciences.
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Martingale transforms and fractional integrals on rearrangement-invariant martingale Hardy spaces
Periodica Mathematica Hungarica, 2020Kwok-Pun Ho
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