Author

# Howard E Taylor

Bio: Howard E Taylor is an academic researcher. The author has contributed to research in topics: Markov decision process & Markov kernel. The author has an hindex of 1, co-authored 1 publications receiving 2928 citations.

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01 Jan 1981

TL;DR: A First Course Algebraic methods in Markov Chains Ratio Theorems of Transition Probabilities and Applications Sums of Independent Random Variables as a Markov Chain Order Statistics, Poisson Processes, and Applications Continuous Time Markov chains Diffusion Processes Compounding Stochastic Processes Fluctuation Theory of Partial Sum of Independent Identically Distributed Random Variable Queueing Processes Miscellaneous Problems Index as discussed by the authors.

Abstract: Preface Preface to A First Course Preface to First Edition Contents of A First Course Algebraic Methods in Markov Chains Ratio Theorems of Transition Probabilities and Applications Sums of Independent Random Variables as a Markov Chain Order Statistics, Poisson Processes, and Applications Continuous Time Markov Chains Diffusion Processes Compounding Stochastic Processes Fluctuation Theory of Partial Sums of Independent Identically Distributed Random Variables Queueing Processes Miscellaneous Problems Index

2,987 citations

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TL;DR: A unified framework for the design and the performance analysis of the algorithms for solving change detection problems and links with the analytical redundancy approach to fault detection in linear systems are established.

Abstract: This book is downloadable from http://www.irisa.fr/sisthem/kniga/. Many monitoring problems can be stated as the problem of detecting a change in the parameters of a static or dynamic stochastic system. The main goal of this book is to describe a unified framework for the design and the performance analysis of the algorithms for solving these change detection problems. Also the book contains the key mathematical background necessary for this purpose. Finally links with the analytical redundancy approach to fault detection in linear systems are established. We call abrupt change any change in the parameters of the system that occurs either instantaneously or at least very fast with respect to the sampling period of the measurements. Abrupt changes by no means refer to changes with large magnitude; on the contrary, in most applications the main problem is to detect small changes. Moreover, in some applications, the early warning of small - and not necessarily fast - changes is of crucial interest in order to avoid the economic or even catastrophic consequences that can result from an accumulation of such small changes. For example, small faults arising in the sensors of a navigation system can result, through the underlying integration, in serious errors in the estimated position of the plane. Another example is the early warning of small deviations from the normal operating conditions of an industrial process. The early detection of slight changes in the state of the process allows to plan in a more adequate manner the periods during which the process should be inspected and possibly repaired, and thus to reduce the exploitation costs.

3,830 citations

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TL;DR: In this article, a unifying theory for valuing contingent claims under a stochastic term structure of interest rates is presented, based on the equivalent martingale measure technique.

Abstract: This paper presents a unifying theory for valuing contingent claims under a stochastic term structure of interest rates. The methodology, based on the equivalent martingale measure technique, takes as given an initial forward rate curve and a family of potential stochastic processes for its subsequent movements. A no arbitrage condition restricts this family of processes yielding valuation formulae for interest rate sensitive contingent claims which do not explicitly depend on the market prices of risk. Examples are provided to illustrate the key results.

2,799 citations

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TL;DR: In this article, Modelling Extremal Events for Insurance and Finance is discussed. But the authors focus on the modeling of extreme events for insurance and finance, and do not consider the effects of cyber-attacks.

Abstract: (2002). Modelling Extremal Events for Insurance and Finance. Journal of the American Statistical Association: Vol. 97, No. 457, pp. 360-360.

2,729 citations

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TL;DR: In this article, the authors present a unifying theory for valuing contingent claims under a stochastic term structure of interest rates, based on the equivalent martingale measure technique.

Abstract: This paper presents a unifying theory for valuing contingent claims under a stochastic term structure of interest rates. The methodology, based on the equivalent martingale measure technique, takes as given an initial forward rate curve and a family of potential stochastic processeE for its subsequent movements. A no arbitrage condition restricts this family of processes yielding valuation formulae for interest rate sensitive contingent claims which do not explicitly depend on the market prices of risk. Examples are provided to illustrate the key results. IN RELATION TO the term structure of interest rates, arbitrage pricing theory has two purposes. The first, is to price all zero coupon (default free) bonds of varying maturities from a finite number of economic fundamentals, called state variables. The second, is to price all interest rate sensitive contingent claims, taking as given the prices of the zero coupon bonds. This paper presents a general theory and a unifying framework for understanding arbitrage pricing theory in this context, of which all existing arbitrage pricing models are special cases (in particular, Vasicek (1977), Brennan and Schwartz (1979), Langetieg (1980), Ball and Torous (1983), Ho and Lee (1986), Schaefer and Schwartz (1987), and Artzner and Delbaen (1988)). The primary contribution of this paper, however, is a new methodology for solving the second problem, i.e., the pricing of interest rate sensitive contingent claims given the prices of all zero coupon bonds. The methodology is new because (i) it imposes its stochastic structure directly on the evolution of the forward rate curve, (ii) it does not require an "inversion of the term structure" to eliminate the market prices of risk from contingent claim values, and (iii) it has a stochastic spot rate process with multiple stochastic factors influencing the term structure. The model can be used to consistently price (and hedge) all contingent claims (American or European) on the term structure, and it is derived from necessary and (more importantly) sufficient conditions for the absence of arbitrage. The arbitrage pricing models of Vasicek (1977), Brennan and Schwartz (1979), Langetieg (1980), and Artzner and Delbaen (1988) all require an IFormerly titled "Bond Pricing and the Term Structure of Interest Rates: A New Methodology."

2,574 citations

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University of Oregon

^{1}, University of California, Berkeley^{2}, University of Washington^{3}, Microsoft^{4}, Oberlin College^{5}TL;DR: Markov Chains and Mixing Times as mentioned in this paper is an introduction to the modern approach to the theory of Markov chains and its application in the field of probability theory and linear algebra, where the main goal is to determine the rate of convergence of a Markov chain to the stationary distribution.

Abstract: This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of random walks on networks, including hitting and cover times, and analyses of several methods of shuffling cards. As a prerequisite, the authors assume a modest understanding of probability theory and linear algebra at an undergraduate level. ""Markov Chains and Mixing Times"" is meant to bring the excitement of this active area of research to a wide audience.

2,573 citations