An Introduction to Continuous-Time Stochastic Processes: Theory, Models, and Applications to Finance, Biology, and Medicine (Modeling and Simulation in Science, Engineering and Technology)

This concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics covered include: * Interacting particles and agent-based models: from polymers to ants * Population dynamics: from birth and death processes to epidemics * Financial market models: the non-arbitrage principle * Contingent claim valuation models: the risk-neutral valuation theory * Risk analysis in insurance An Introduction to Continuous-Time Stochastic Processes will be of interest to a broad audience of students, pure and applied mathematicians, and researchers or practitioners in mathematical finance, biomathematics, biotechnology, and engineering. Suitable as a textbook for graduate or advanced undergraduate courses, the work may also be used for self-study or as a reference. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. This book is a systematic, rigorous, and self-consistent introduction to the theory of continuous-time stochastic processes. But it is neither a tract nor a recipe book as such; rather, it is an account of fundamental concepts as they appear in relevant modern applications and literature. We make no pretense of it being complete. Indeed, we have omitted many results, which we feel are notdirectly relatedtothemain themeorthatare availablein easilyaccessible sources. (Thosereaderswhoareinterestedinthehistoricaldevelopmentofthe subject cannot ignore the volume edited by Wax (1954).) Proofs are often omitted as technicalities might distract the reader from a conceptual approach. They are produced whenever they may serve as a guide to the introduction of new concepts and methods towards the app- cations; otherwise, explicit references to standard literature are provided. A mathematically oriented student may?nd it interesting to consider proofs as exercises. The scope of the book is profoundly educational, related to modeling re- world problems with stochastic methods. The reader becomes critically aware oftheconceptsinvolvedincurrentappliedliterature,andismoreoverprovided with a?rm foundation of the mathematical techniques. Intuition is always supported by mathematical rigor. Our book addresses three main groups:?rst, mathematicians working in a di?erent?eld; second, other scientists and professionals from a business or academic background; third, graduate or advanced undergraduate students of a quantitative subject related to stochastic theory and/or applications.

this Concisely Written Book Is A Rigorous And Self-contained Introduction To The Theory Of Continuous-time Stochastic Processes. A Balance Of Theory And Applications, The Work Features Concrete Examples Of Modeling Real-world Problems From Biology, Medicine, Industrial Applications, Finance, And Insurance Using Stochastic Methods. No Previous Knowledge Of Stochastic Processes Is Required.

key Topics Covered Include:

* Interacting Particles And Agent-based Models: From Polymers To Ants

* Population Dynamics: From Birth And Death Processes To Epidemics

* Financial Market Models: The Non-arbitrage Principle

* Contingent Claim Valuation Models: The Risk-neutral Valuation Theory

* Risk Analysis In Insurance

an Introduction To Continuous-time Stochastic Processes Will Be Of Interest To A Broad Audience Of Students, Pure And Applied Mathematicians, And Researchers Or Practitioners In Mathematical Finance, Biomathematics, Biotechnology, And Engineering. Suitable As A Textbook For Graduate Or Advanced Undergraduate Courses, The Work May Also Be Used For Self-study Or As A Reference. Prerequisites Include Knowledge Of Calculus And Some Analysis; Exposure To Probability Would Be Helpful But Not Required Since The Necessary Fundamentals Of Measure And Integration Are Provided.

This concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics covered include: \* Population dynamics: from birth and death processes to epidemics \* Financial market models: the non-arbitrage principle \* Contingent claim valuation models: the risk-neutral valuation theory \* Risk analysis in insurance __An Introduction to Continuous-Time Stochastic Processes__ will be of interest to a broad audience of students, pure and applied mathematicians, and researchers or practitioners in mathematical finance, biomathematics, biotechnology, and engineering. Suitable as a textbook for graduate or advanced undergraduate courses, the work may also be used for self-study or as a reference. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. "This book is an introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods." "An Introduction to Continuous-Time Stochastic Processes will be of interest to a broad audience of students, pure and applied mathematicians, and researchers or practitioners in mathematical finance, biomathematics, biotechnology, physics, and engineering. Suitable as a textbook for graduate or advanced undergraduate courses, the work may also be used for self-study or as a reference."--Jacket This concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. Balancing theory and applications, the authors use stochastic methods and concrete examples to model real-world problems from engineering, biomathematics, biotechnology, and finance. Suitable as a textbook for graduate or advanced undergraduate courses, the work may also be used for self-study or as a reference. The book will be of interest to students, pure and applied mathematicians, and researchers or practitioners in mathematical finance, biomathematics, physics, and engineering. Front Matter....Pages 1-1 Fundamentals of Probability....Pages 3-50 Stochastic Processes....Pages 51-126 The Itô Integral....Pages 127-159 Stochastic Differential Equations....Pages 161-208 Front Matter....Pages 209-209 Applications to Finance and Insurance....Pages 211-238 Applications to Biology and Medicine....Pages 239-279 We assume that the reader is already familiar with the basic motivations and notions of probability theory.