Random Iterative Models (Stochastic Modelling and Applied Probability)

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Stochastic Models in Reliability

In the second part of the thesis, we consider a framework called manifold sampling, intended for unconstrained DFO problems where the objective is nonsmooth, but enough is known a priori about the structure of the nonsmoothness that one can classify a given queried point as belonging to a certain smooth manifold of the objective surface. We particularly examine the case of sums of absolute values of non-convex black-box functions.

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Stochastic optimization

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Book Description Springer. Seller Inventory NEW Seller Inventory ING KG, Germany, Language: English. Brand new Book. An up-to-date, self-contained review of a wide range of recursive methods for stabilization, identification and control of complex stochastic models guiding a rocket or a plane, organizing multi-access broadcast channels, self-learning of neural networks.

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Marie Duflo. Publisher: Springer , This is due to the availability of ultra high frequency data in financial markets, which is much more informative than the classical daily observations scheme. One of the main focuses in financial econometrics is the volatility process, a measure of the variability, which can be statistically recovered from high frequency observations of an asset price. This lecture aims at demonstrating and explaining the limit theory for high frequency observations of semimartingales a standard model in finance , presenting the classical estimation and testing procedures, and covering some future challenges.

In the first part of the lecture we will learn the notion of stable convergence and derive some asymptotic results for high frequency statistics of semimartingales in the purely continuous and jump settings.

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In the second part we will concentrate on classical testing and estimation methods, including estimation of integrated or local volatility, testing for jumps, and estimation of the asymptotic variances among other problems. However, at the very high frequency, the traditional statistical models do not appear to be rich enough.

The lecture discusses a generalization of the omnipresent Ito semimartingale which incorporates the possibility of zeros. We show this has a huge impact on the measurement of volatility, jumps and important implications for asset pricing. We complement the statistical model with an economic model in which agents with different levels of information interact in a market with costly transactions.

Laruelle , Pagès : Nonlinear randomized urn models: a stochastic approximation viewpoint

The model is able to generate zero returns in the data. We discuss some testable implications of the model linking zeros to trading volume, volatility and transaction costs. Flash crashes slides While the literature on high-frequency data almost exclusively concentratated on variation measures volatility and jumps , flash crashes need a drift dominating over volatility, that is an exploding drift. The lecture will discuss the "Drift Burst Hypothesis" and its consequences for arbitrage.

Past Seminars

With the drift burst hypothesis in place and the corresponding Ito semimartingale price process specified, we develop an effective identification strategy for the on-line detection of drift burst sample paths from intraday noisy high-frequency data.