Stochastic methods

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  • A considerable part of the vast development in Mathematical Finance over the last two decades was determined by the application of stochastic methods. These were therefore chosen as the focus of the 2003 School on “Stochastic Methods in Finance”. The growing interest of the mathematical community in this field was also reflected by the extraordinarily high number of applications for the CIME-EMS School. It was attended by 115 scientists and researchers, selected from among over 200 applicants. The attendees came from all continents: 85 were Europeans, among them 35 Italians.

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  • Stochastic Optimization Algorithms have become essential tools in solving a wide range of difficult and critical optimization problems. Such methods are able to find the optimum solution of a problem with uncertain elements or to algorithmically incorporate uncertainty to solve a deterministic problem. They even succeed in “fighting uncertainty with uncertainty”. This book discusses theoretical aspects of many such algorithms and covers their application in various scientific fields

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  • IT IS WELL KNOWN that Western languages are 50% redundant. Experiment shows that if an average person guesses the successive words in a completely unknown sentence he has to be told only half of them. Experiment shows that this also applies to guessing the successive word-ideas in a foreign language.

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  • While the stochastic volatility (SV) generalization has been shown to improve the explanatory power over the Black-Scholes model, empirical implications of SV models on option pricing have not yet been adequately tested. The purpose of this paper is to first estimate a multivariate SV model using the efficient method of moments (EMM) technique from observations of underlying state variables and then investigate the respective effect of stochastic interest rates, systematic volatility and idiosyncratic volatility on option prices....

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  • Basic principles underlying the transactions of financial markets are tied to probability and statistics. Accordingly it is natural that books devoted to mathematical finance are dominated by stochastic methods. Only in recent years, spurred by the enormous economical success of financial derivatives, a need for sophisticated computational technology has developed. For example, to price an American put, quantitative analysts have asked for the numerical solution of a free-boundary partial differential equation.

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  • This book presents and develops major numerical methods currently used for solving problems arising in quantitative finance. Our presentation splits into two parts. Part I is methodological, and offers a comprehensive toolkit on numerical methods and algorithms. This includes Monte Carlo simulation, numerical schemes for partial differential equations, stochastic optimization in discrete time, copula functions, transform-based methods and quadrature techniques. Part II is practical, and features a number of self-contained cases.

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  • This article presents the stochastic growth model. The stochastic growth model is a stochastic version of the neoclassical growth model with microfoundations,1 and provides the backbone of a lot of macroeconomic models that are used in modern macroeconomic research. The most popular way to solve the stochastic growth model, is to linearize the model around a steady state,2 and to solve the linearized model with the method of undetermined coefficients. This solution method is due to Campbell (1994)....

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  • The 3 billion base pair sequence of the human genome is now available, and attention is focusing on annotating it to extract biological meaning. I will discuss what we have obtained, and the methods that are being used to analyse biological sequences. In particular I will discuss approaches using stochastic grammars analogous to those used in computational linguistics, both for gene finding and protein family classification.

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  • This paper discusses the supervised learning of morphology using stochastic transducers, trained using the ExpectationMaximization (EM) algorithm. Two approaches are presented: first, using the transducers directly to model the process, and secondly using them to define a similarity measure, related to the Fisher kernel method (Jaakkola and Haussler, 1998), and then using a Memory-Based Learning (MBL) technique. These are evaluated and compared on data sets from English, German, Slovene and Arabic. ...

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  • A description will be given of a procedure to asslgn the most likely probabilitles to each of the rules of a given context-free grammar. The grammar developed by S. Kuno at Harvard University was picked as the basis and was successfully augmented with rule probabilities. A brief exposition of the method with some preliminary results, w h e n u s e d as a device for disamblguatingparsing English texts picked from natural corpus, will be given.

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  • Stochastic control plays an important role in many scientific and applied disciplines including communications, engineering, medicine, finance and many others. It is one of the effective methods being used to find optimal decision-making strategies in applications. The book provides a collection of outstanding investigations in various aspects of stochastic systems and their behavior. The book provides a self-contained treatment on practical aspects of stochastic modeling and calculus including applications drawn from engineering, statistics, and computer science....

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  • Lagerhaltung dient im Allgemeinen der Anpassung von Angebots- und Nachfrageprozessen, die nicht zusammen passen. So beschreibt es Paul Zipkin in seinem Buch Foundations of Inventory Management [94] sehr treffend. Ziel ist es also die Produktions- oder Beschaffungsabläufe mit den Nachfrageprozessen zu verheiraten, ohne dass es zu Problemen in den Kundenbeziehungen kommt, weil nachgefragte Teile nicht geliefert werden können. Lager dienen als Puffer, der in Zeiten geringer Nachfrage die Überproduktion aufnimmt und in Zeiten besonders starker Nachfrage die Unterproduktion ausgleicht.

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  • To study PP attachment disambiguation as a benchmark for empirical methods in natural language processing it has often been reduced to a binary decision problem (between verb or noun attachment) in a particular syntactic configuration. A parser, however, must solve the more general task of deciding between more than two alternatives in many different contexts. We combine the attachment predictions made by a simple model of lexical attraction with a full-fledged parser of German to determine the actual benefit of the subtask to parsing.

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  • Stochastic Optimality Theory (Boersma, 1997) is a widely-used model in linguistics that did not have a theoretically sound learning method previously. In this paper, a Markov chain Monte-Carlo method is proposed for learning Stochastic OT Grammars. Following a Bayesian framework, the goal is finding the posterior distribution of the grammar given the relative frequencies of input-output pairs. The Data Augmentation algorithm allows one to simulate a joint posterior distribution by iterating two conditional sampling steps. ...

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  • We present a stochastic finite-state model for segmenting Chinese text into dictionary entries and productively derived words, and providing pronunciations for these words; the method incorporates a class-based model in its treatment of personal names. We also evaluate the system's performance, taking into account the fact that people often do not agree on a single segmentation.

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  • We present an algorithm for computing n-gram probabilities from stochastic context-free grammars, a procedure that can alleviate some of the standard problems associated with n-grams (estimation from sparse data, lack of linguistic structure, among others). The method operates via the computation of substring expectations, which in turn is accomplished by solving systems of linear equations derived from the grammar. The procedure is fully implemented and has proved viable and useful in practice. confirming its practical feasibility and utility.

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  • This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers. Subjects covered include Brownian motion, stochastic calculus, stochastic differential equations, Markov processes, weak convergence of processes, and semigroup theory.

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  • In panel data models (as in single-equation multiple-regression models) we are interested in testing two types of hypotheses: hypotheses about the variances and covariances of the stochastic error terms and hypotheses about the regression coefficients. The general to simple procedure provides a good guide.

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  • inaccuracies lead to the deviation of operational space trajectory provided by the kinematic mapping. One method to deal with this issue can be found in an adaptive control. Xu and Gu proposed an adaptive control scheme for space robots in both joint space and operational space [Xu et al., 1992, Gu & Xu, 1993]. However, the adaptive control proposed in [Xu et al., 1992] requires perfect attitude control and the adaptive control in [Gu & Xu, 1993] is developed based on an under-actuated system on the assumption that the acceleration of the base-satellite is measurable.

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  • ADVANCED TEXTS IN ECONOMETRICS General Editors Manuel Arellano Guido Imbens Grayham E. Mizon Adrian Pagan Mark Watson Advisory Editor C. W. J. Granger.Other Advanced Texts in conometrics ARCH: Selected Readings Edited by Robert F. Engle Asymptotic Theory for Integrated Processes By H. Peter Boswijk Bayesian Inference in Dynamic Econometric Models By Luc Bauwens, Michel Lubrano, and Jean-Fran¸ois Richard c Co-tegration, Error Correction, and the Econometric Analysis of Non-Stationary Data By Anindya Banerjee, Juan J. ...

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