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Author : Liqun Wang
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.:/5 (314 download)
Download or read book Boundary Crossing Probability for Brownian Motion and General Boundaries written by Liqun Wang and published by . This book was released on 1994 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tung-Lung Wu (Jr.)
Publisher :
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.:/5 (855 download)
Download or read book Linear and Non-linear Boundary Crossing Probabilities for Brownian Motion and Related Processes written by Tung-Lung Wu (Jr.) and published by . This book was released on 2012 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a simple and general method to obtain the boundary crossing probability for Brownian motion. This method can be easily extended to higher dimensional of Brownian motion. It also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a nite Markov chain such that the boundary crossing probability of Brownian motion is obtained as the limiting probability of the nite Markov chain entering a set of absorbing states induced by the boundary. Numerical results are given to illustrate our method.
Author : Hans R. Lerche
Publisher : Springer Science & Business Media
ISBN 13 : 1461565693
Total Pages : 147 pages
Book Rating : 4.4/5 (615 download)
Download or read book Boundary Crossing of Brownian Motion written by Hans R. Lerche and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a research report about my work on sequential statistic~ during 1980 - 1984. Two themes are treated which are closely related to each other and to the law of the iterated logarithm:· I) curved boundary first passage distributions of Brownian motion, 11) optimal properties of sequential tests with parabolic and nearly parabolic boundaries. In the first chapter I discuss the tangent approximation for Brownianmotion as a global approximation device. This is an extension of Strassen' s approach to t'he law of the iterated logarithm which connects results of fluctuation theory of Brownian motion with classical methods of sequential statistics. In the second chapter I make use of these connections and derive optimal properties of tests of power one and repeated significance tests for the simpiest model of sequential statistics, the Brownian motion with unknown drift. To both topics:there under1ies an asymptotic approach which is closely linked to large deviation theory: the stopping boundaries recede to infinity. This is a well-known approach in sequential stötistics which is extensively discussed in Siegmund's recent book ·Sequential Analysis". This approach also leads to some new insights about the law of the iterated logarithm (LIL). Although the LIL has been studied for nearly seventy years the belief is still common that it applies only for large sampIe sizes which can never be obser ved in practice.
Author : Tung-Lung Jr Wu
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (135 download)
Download or read book Linear and Non-linear Boundary Crossing Probabilities for Brownian Motion and Related Processes written by Tung-Lung Jr Wu and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a simple and general method to obtain the boundary crossing probability for Brownian motion. This method can be easily extended to higher dimensional of Brownian motion. It also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a nite Markov chain such that the boundary crossing probability of Brownian motion is obtained as the limiting probability of the nite Markov chain entering a set of absorbing states induced by the boundary. Numerical results are given to illustrate our method.
Author : Zhiyong Jin
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (135 download)
Download or read book A New Approach to the Computation of First Passage Time Distribution for Brownian Motion written by Zhiyong Jin and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis consists of two novel contributions to the computation of first passage time distribution for Brownian motion. First, we extend the known formula for boundary crossing probabilities for Brownian motion to the discontinuous piecewise linear boundary. Second, we derive explicit formula for the first passage time density of Brownian motion crossing piecewise linear boundary. Further, we demonstrate how to approximate the boundary crossing probabilities and density for general nonlinear boundaries. Moreover, we use Monte Carlo simulation method and develop algorithms for the numerical computation. This method allows one to assess the accuracy of the numerical approximation. Our approach can be further extended to compute two-sided boundary crossing probabilities.
Author : STANFORD UNIV CA DEPT OF STATISTICS.
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (123 download)
Download or read book Boundary Crossing Probabilities and Statistical Applications written by STANFORD UNIV CA DEPT OF STATISTICS. and published by . This book was released on 1985 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper surveys recent results involving boundary crossing probabilities and related statistical applications. The first part is concerned with problems of sequential analysis, especially repeated significance tests and their application to sequential clinical trials involving survival data. The second part develops the probability theory motivated by the problems of Part 1. A method for computing first passage distributions of Brownian motion to linear boundaries is introduced and then modified to handle problems in discrete time and those involving nonlinear boundaries. The third part is concerned with fixed sample statistical problems, especially change-point problems, which involve boundary crossing probabilities. Examples are given of problems for which methods of Part 2 appear adequate and of problems which require new methods.
Author : Carl Chiarella
Publisher : Springer Science & Business Media
ISBN 13 : 3642034780
Total Pages : 421 pages
Book Rating : 4.6/5 (42 download)
Download or read book Contemporary Quantitative Finance written by Carl Chiarella and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers dedicated to Professor Eckhard Platen to celebrate his 60th birthday, which occurred in 2009. The contributions have been written by a number of his colleagues and co-authors. All papers have been - viewed and presented as keynote talks at the international conference “Quantitative Methods in Finance” (QMF) in Sydney in December 2009. The QMF Conference Series was initiated by Eckhard Platen in 1993 when he was at the Australian - tional University (ANU) in Canberra. Since joining UTS in 1997 the conference came to be organised on a much larger scale and has grown to become a signi?cant international event in quantitative ?nance. Professor Platen has held the Chair of Quantitative Finance at the University of Technology, Sydney (UTS) jointly in the Faculties of Business and Science since 1997. Prior to this appointment, he was the Founding Head of the Centre for Fin- cial Mathematics at the Institute of Advanced Studies at ANU, a position to which he was appointed in 1994. Eckhard completed a PhD in Mathematics at the Technical University in Dresden in 1975 and in 1985 obtained his Doctor of Science degree (Habilitation degree in the German system) from the Academy of Sciences in Berlin where he headed the Stochastics group at the Weierstrass Institute.
Author :
Publisher :
ISBN 13 :
Total Pages : 634 pages
Book Rating : 4.3/5 (91 download)
Download or read book Journal of Applied Probability written by and published by . This book was released on 2001 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andrey Sarychev
Publisher : Springer Science & Business Media
ISBN 13 : 354069532X
Total Pages : 418 pages
Book Rating : 4.5/5 (46 download)
Download or read book Mathematical Control Theory and Finance written by Andrey Sarychev and published by Springer Science & Business Media. This book was released on 2009-03-31 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control theory provides a large set of theoretical and computational tools with applications in a wide range of ?elds, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to ?nd solutions to ”real life” problems, as is the case in robotics, control of industrial processes or ?nance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the ?nancial analyst to possess a high level of mathematical skills. C- versely, the complex challenges posed by the problems and models relevant to ?nance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical ?nance. Up to now, other branches of control theory have found comparatively less application in ?n- cial problems. To some extent, deterministic and stochastic control theories developed as di?erent branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these ?elds has intensi?ed. Some concepts from stochastic calculus (e.g., rough paths) havedrawntheattentionofthedeterministiccontroltheorycommunity.Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic c- trol.
Author : Michael Falk
Publisher : Springer Science & Business Media
ISBN 13 : 3034800096
Total Pages : 513 pages
Book Rating : 4.0/5 (348 download)
Download or read book Laws of Small Numbers: Extremes and Rare Events written by Michael Falk and published by Springer Science & Business Media. This book was released on 2010-10-07 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results. In this third edition, the dramatic change of focus of extreme value theory has been taken into account: from concentrating on maxima of observations it has shifted to large observations, defined as exceedances over high thresholds. One emphasis of the present third edition lies on multivariate generalized Pareto distributions, their representations, properties such as their peaks-over-threshold stability, simulation, testing and estimation. Reviews of the 2nd edition: "In brief, it is clear that this will surely be a valuable resource for anyone involved in, or seeking to master, the more mathematical features of this field." David Stirzaker, Bulletin of the London Mathematical Society "Laws of Small Numbers can be highly recommended to everyone who is looking for a smooth introduction to Poisson approximations in EVT and other fields of probability theory and statistics. In particular, it offers an interesting view on multivariate EVT and on EVT for non-iid observations, which is not presented in a similar way in any other textbook." Holger Drees, Metrika
Author : Thomas H. Scheike
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (912 download)
Download or read book Working paper written by Thomas H. Scheike and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Falk
Publisher : Springer Science & Business Media
ISBN 13 : 9783764324162
Total Pages : 396 pages
Book Rating : 4.3/5 (241 download)
Download or read book Laws Of Small Numbers written by Michael Falk and published by Springer Science & Business Media. This book was released on 2004 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results on about 130 additional pages. Part II, which has been added in the second edition, discusses recent developments in multivariate extreme value theory. Particularly notable is a new spectral decomposition of multivariate distributions in univariate ones which makes multivariate questions more accessible in theory and practice. One of the most innovative and fruitful topics during the last decades was the introduction of generalized Pareto distributions in the univariate extreme value theory. Such a statistical modelling of extremes is now systematically developed in the multivariate framework.
Author : Joseph L. Doob
Publisher :
ISBN 13 :
Total Pages : 86 pages
Book Rating : 4.3/5 (91 download)
Download or read book Conditional Brownian Motion and the Boundary Limits of Harmonic Functions written by Joseph L. Doob and published by . This book was released on 1957 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Thomas H. Scheike
Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (315 download)
Download or read book A Boundary Crossing Result for the Brownian Motion written by Thomas H. Scheike and published by . This book was released on 1990 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wolfgang Bischoff
Publisher :
ISBN 13 :
Total Pages : 7 pages
Book Rating : 4.:/5 (13 download)
Download or read book A Lower Bound for Boundary Crossing Probabilities of Brownian Bridge written by Wolfgang Bischoff and published by . This book was released on 2018 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter Mörters
Publisher : Cambridge University Press
ISBN 13 : 1139486578
Total Pages : pages
Book Rating : 4.1/5 (394 download)
Download or read book Brownian Motion written by Peter Mörters and published by Cambridge University Press. This book was released on 2010-03-25 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.
Author : Santiago Moreno-Bromberg
Publisher : Princeton University Press
ISBN 13 : 1400889200
Total Pages : 176 pages
Book Rating : 4.4/5 (8 download)
Download or read book Continuous-Time Models in Corporate Finance, Banking, and Insurance written by Santiago Moreno-Bromberg and published by Princeton University Press. This book was released on 2018-01-08 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous-Time Models in Corporate Finance synthesizes four decades of research to show how stochastic calculus can be used in corporate finance. Combining mathematical rigor with economic intuition, Santiago Moreno-Bromberg and Jean-Charles Rochet analyze corporate decisions such as dividend distribution, the issuance of securities, and capital structure and default. They pay particular attention to financial intermediaries, including banks and insurance companies. The authors begin by recalling the ways that option-pricing techniques can be employed for the pricing of corporate debt and equity. They then present the dynamic model of the trade-off between taxes and bankruptcy costs and derive implications for optimal capital structure. The core chapter introduces the workhorse liquidity-management model—where liquidity and risk management decisions are made in order to minimize the costs of external finance. This model is used to study corporate finance decisions and specific features of banks and insurance companies. The book concludes by presenting the dynamic agency model, where financial frictions stem from the lack of interest alignment between a firm's manager and its financiers. The appendix contains an overview of the main mathematical tools used throughout the book. Requiring some familiarity with stochastic calculus methods, Continuous-Time Models in Corporate Finance will be useful for students, researchers, and professionals who want to develop dynamic models of firms' financial decisions.
