selected topics on continuous time controlled markov chains and markov games

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Selected Topics On Continuous Time Controlled Markov Chains And Markov Games

Author : Tomás Prieto-Rumeau
ISBN : 9781908977632
Genre : Mathematics
File Size : 20. 72 MB
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This book concerns continuous-time controlled Markov chains, also known as continuous-time Markov decision processes. They form a class of stochastic control problems in which a single decision-maker wishes to optimize a given objective function. This book is also concerned with Markov games, where two decision-makers (or players) try to optimize their own objective function. Both decision-making processes appear in a large number of applications in economics, operations research, engineering, and computer science, among other areas. An extensive, self-contained, up-to-date analysis of basic optimality criteria (such as discounted and average reward), and advanced optimality criteria (e.g., bias, overtaking, sensitive discount, and Blackwell optimality) is presented. A particular emphasis is made on the application of the results herein: algorithmic and computational issues are discussed, and applications to population models and epidemic processes are shown. This book is addressed to students and researchers in the fields of stochastic control and stochastic games. Moreover, it could be of interest also to undergraduate and beginning graduate students because the reader is not supposed to have a high mathematical background: a working knowledge of calculus, linear algebra, probability, and continuous-time Markov chains should suffice to understand the contents of the book. Contents:IntroductionControlled Markov ChainsBasic Optimality CriteriaPolicy Iteration and Approximation TheoremsOvertaking, Bias, and Variance OptimalitySensitive Discount OptimalityBlackwell OptimalityConstrained Controlled Markov ChainsApplicationsZero-Sum Markov GamesBias and Overtaking Equilibria for Markov Games Readership: Graduate students and researchers in the fields of stochastic control and stochastic analysis. Keywords:Markov Decision Processes;Continuous-Time Controlled Markov Chains;Stochastic Dynamic Programming;Stochastic GamesKey Features:This book presents a reader-friendly, extensive, self-contained, and up-to-date analysis of advanced optimality criteria for continuous-time controlled Markov chains and Markov games. Most of the material herein is quite recent (it has been published in high-impact journals during the last five years) and it appears in book form for the first timeThis book introduces approximation theorems which, in particular, allow the reader to obtain numerical approximations of the solution to several control problems of practical interest. To the best of our knowledge, this is the first time that such computational issues are studied for denumerable state continuous-time controlled Markov chains. Hence, the book has an adequate balance between, on the one hand, theoretical results and, on the other hand, applications and computational issuesThe books that analyze continuous-time controlled Markov chains usually restrict themselves to the case of bounded transition and reward rates, which can be reduced to discrete-time models by using the uniformization technique. In our case, however, the transition and the reward rates might be unbounded, and so the uniformization technique cannot be used. By the way, let us mention that in models of practical interest the transition and the reward rates are, typically, unboundedReviews:“The book contains a large number of recent research results on CMCs and Markov games and puts them in perspective. It is written in a very conscious manner, contains detailed proofs of all main results, as well as extensive bibliographic remarks. The book is a very valuable piece of work for researchers on continuous-time CMCs and Markov games.”Zentralblatt MATH

Optimization Control And Applications Of Stochastic Systems

Author : Daniel Hernández-Hernández
ISBN : 9780817683375
Genre : Science
File Size : 45. 86 MB
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This volume provides a general overview of discrete- and continuous-time Markov control processes and stochastic games, along with a look at the range of applications of stochastic control and some of its recent theoretical developments. These topics include various aspects of dynamic programming, approximation algorithms, and infinite-dimensional linear programming. In all, the work comprises 18 carefully selected papers written by experts in their respective fields. Optimization, Control, and Applications of Stochastic Systems will be a valuable resource for all practitioners, researchers, and professionals in applied mathematics and operations research who work in the areas of stochastic control, mathematical finance, queueing theory, and inventory systems. It may also serve as a supplemental text for graduate courses in optimal control and dynamic games.

Arbitrage Credit And Informational Risks

Author : Caroline Hillairet
ISBN : 9789814602082
Genre : Mathematics
File Size : 63. 77 MB
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This book contains a collection of research papers in mathematical finance covering recent advances in arbitrage, credit and asymmetric information risks. These subjects have attracted academic and practical attention, in particular after the international financial crisis. The volume is split into three parts which treat each of these topics. Contents:Arbitrage:No-arbitrage Conditions and Absolutely Continuous Changes of Measure (Claudio Fontana)A Systematic Approach to Constructing Market Models with Arbitrage (Johannes Ruf and Wolfgang J Runggaldier)On the Existence of Martingale Measures in Jump Diffusion Market Models (Jacopo Mancin and Wolfgang J Runggaldier)Arbitrages in a Progressive Enlargement Setting (Anna Aksamit, Tahir Choulli, Jun Deng and Monique Jeanblanc)Credit Risk:Pricing Credit Derivatives with a Structural Default Model (Sébastien Hitier and Ying Zhu)Reduced-Form Modeling of Counterparty Risk on Credit Derivatives (Stéphane Crépey)Dynamic One-default Model (Shiqi Song)Stochastic Sensitivity Study for Optimal Credit Allocation (Laurence Carassus and Simone Scotti)Control Problem and Information Risks:Discrete-Time Multi-Player Stopping and Quitting Games with Redistribution of Payoffs (Ivan Guo and Marek Rutkowski)A Note on BSDEs with Singular Driver Coefficients (Monique Jeanblanc and Anthony Réveillac)A Portfolio Optimization Problem with Two Prices Generated by Two Information Flows (Caroline Hillairet)Option Pricing under Stochastic Volatility, Jumps and Cost of Information (Sana Mahfoudh and Monique Pontier) Readership: Advanced undergraduates, graduates and researchers in financial mathematics. Key Features:Treats new problems and challenges issued from the recent financial crisis and proposes original research papers on the modeling and management of the related financial risks, notably the credit risk and information asymmetry risksThe contributors consist of worldwide renowned experts and also promising young scientists in financial mathematicsAccessible to a larger public including graduate and advanced undergraduate studentsKeywords:Arbitrage;Credit Risk;Information Asymmetry Risks

Advances In Applied Probability

Author :
ISBN : UCSD:31822036043701
Genre : Probabilities
File Size : 50. 68 MB
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Methods And Applications Of White Noise Analysis In Interdisciplinary Sciences

Author : Christopher C Bernido
ISBN : 9789814569132
Genre : Mathematics
File Size : 75. 7 MB
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Analysis, modeling, and simulation for better understanding of diverse complex natural and social phenomena often require powerful tools and analytical methods. Tractable approaches, however, can be developed with mathematics beyond the common toolbox. This book presents the white noise stochastic calculus, originated by T Hida, as a novel and powerful tool in investigating physical and social systems. The calculus, when combined with Feynman's summation-over-all-histories, has opened new avenues for resolving cross-disciplinary problems. Applications to real-world complex phenomena are further enhanced by parametrizing non-Markovian evolution of a system with various types of memory functions. This book presents general methods and applications to problems encountered in complex systems, scaling in industry, neuroscience, polymer physics, biophysics, time series analysis, relativistic and nonrelativistic quantum systems. Contents:IntroductionWhite Noise Analysis: Some Basic Notions and TerminologyFluctuations with MemoryComplex SystemsTime Series AnalysisFluctuations without MemoryNeurophysicsBiopolymersWhite Noise Functional Integrals in Quantum MechanicsQuantum Particles with Boundary ConditionsRelativistic Quantum Mechanics Readership: Researchers in stochastic analysis, mathematical modeling and complex systems. Keywords:White Noise Analysis;Fractional Brownian Motion;Fluctuation With Memory;Complex Systems;Neurophysics;Biopolymers;Time Series Analysis;Path Integral;Quantum SystemsKey Features:White noise analysis is a relatively young mathematical research area. This volume will present and demonstrate how this new, powerful mathematical tool can be effectively utilized and applied to current problems in the interdisciplinary sciencesIt combines white noise analysis with the equally powerful Feynman path integral, thus allowing us to track the evolution even of systems with memory and strong correlationsIt is user-friendly

Markov Chains

Author : J. R. Norris
ISBN : 0521633966
Genre : Mathematics
File Size : 57. 20 MB
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In this rigorous account the author studies both discrete-time and continuous-time chains. A distinguishing feature is an introduction to more advanced topics such as martingales and potentials, in the established context of Markov chains. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and a careful selection of exercises and examples drawn both from theory and practice. This is an ideal text for seminars on random processes or for those that are more oriented towards applications, for advanced undergraduates or graduate students with some background in basic probability theory.

Essentials Of Stochastic Processes

Author : Richard Durrett
ISBN : 9781461436157
Genre : Mathematics
File Size : 86. 37 MB
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This book is for a first course in stochastic processes taken by undergraduates or master’s students who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and mathematical finance. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding The book has undergone a thorough revision since the first edition. There are many new examples and problems with solutions that use the TI-83 to eliminate the tedious details of solving linear equations by hand. Some material that was too advanced for the level has been eliminated while the treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved. For example, the difficult subject of martingales is delayed until its usefulness can be seen in the treatment of mathematical finance. Richard Durrett received his Ph.D. in Operations Research from Stanford in 1976. He taught at the UCLA math department for nine years and at Cornell for twenty-five before moving to Duke in 2010. He is the author of 8 books and almost 200 journal articles, and has supervised more that 40 Ph.D. students. Most of his current research concerns the applications of probability to biology: ecology, genetics, and most recently cancer.

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