Fima C Klebaner – författare

Problems and Solutions in Stochastic Calculus with Applications exposes readers to simple ideas and proofs in stochastic calculus and its applications. It is intended as a companion to the successful original title Introduction to Stochastic Calculus with Applications (Third Edition) by Fima Klebaner. The current book is authored by three active researchers in the fields of probability, stochastic processes, and their applications in financial mathematics, mathematical biology, and more. The book features problems rooted in their ongoing research. Mathematical finance and biology feature pre-eminently, but the ideas and techniques can equally apply to fields such as engineering and economics.The problems set forth are accessible to students new to the subject, with most of the problems and their solutions centring on a single idea or technique at a time to enhance the ease of learning. While the majority of problems are relatively straightforward, more complex questions are also set in order to challenge the reader as their understanding grows. The book is suitable for either self-study or for instructors, and there are numerous opportunities to generate fresh problems by modifying those presented, facilitating a deeper grasp of the material.

Problems and Solutions in Stochastic Calculus with Applications exposes readers to simple ideas and proofs in stochastic calculus and its applications. It is intended as a companion to the successful original title Introduction to Stochastic Calculus with Applications (Third Edition) by Fima Klebaner. The current book is authored by three active researchers in the fields of probability, stochastic processes, and their applications in financial mathematics, mathematical biology, and more. The book features problems rooted in their ongoing research. Mathematical finance and biology feature pre-eminently, but the ideas and techniques can equally apply to fields such as engineering and economics.The problems set forth are accessible to students new to the subject, with most of the problems and their solutions centring on a single idea or technique at a time to enhance the ease of learning. While the majority of problems are relatively straightforward, more complex questions are also set in order to challenge the reader as their understanding grows. The book is suitable for either self-study or for instructors, and there are numerous opportunities to generate fresh problems by modifying those presented, facilitating a deeper grasp of the material.

This book presents a concise and rigorous treatment of stochastic calculus. It also gives its main applications in finance, biology and engineering. In finance, the stochastic calculus is applied to pricing options by no arbitrage. In biology, it is applied to populations' models, and in engineering it is applied to filter signal from noise. Not everything is proved, but enough proofs are given to make it a mathematically rigorous exposition.This book aims to present the theory of stochastic calculus and its applications to an audience which possesses only a basic knowledge of calculus and probability. It may be used as a textbook by graduate and advanced undergraduate students in stochastic processes, financial mathematics and engineering. It is also suitable for researchers to gain working knowledge of the subject. It contains many solved examples and exercises making it suitable for self study.In the book many of the concepts are introduced through worked-out examples, eventually leading to a complete, rigorous statement of the general result, and either a complete proof, a partial proof or a reference. Using such structure, the text will provide a mathematically literate reader with rapid introduction to the subject and its advanced applications. The book covers models in mathematical finance, biology and engineering. For mathematicians, this book can be used as a first text on stochastic calculus or as a companion to more rigorous texts by a way of examples and exercises.

This book presents a concise and rigorous treatment of stochastic calculus. It also gives its main applications in finance, biology and engineering. In finance, the stochastic calculus is applied to pricing options by no arbitrage. In biology, it is applied to populations' models, and in engineering it is applied to filter signal from noise. Not everything is proved, but enough proofs are given to make it a mathematically rigorous exposition.This book aims to present the theory of stochastic calculus and its applications to an audience which possesses only a basic knowledge of calculus and probability. It may be used as a textbook by graduate and advanced undergraduate students in stochastic processes, financial mathematics and engineering. It is also suitable for researchers to gain working knowledge of the subject. It contains many solved examples and exercises making it suitable for self study.In the book many of the concepts are introduced through worked-out examples, eventually leading to a complete, rigorous statement of the general result, and either a complete proof, a partial proof or a reference. Using such structure, the text will provide a mathematically literate reader with rapid introduction to the subject and its advanced applications. The book covers models in mathematical finance, biology and engineering. For mathematicians, this book can be used as a first text on stochastic calculus or as a companion to more rigorous texts by a way of examples and exercises.

This book provides a concise introduction to stochastic calculus with some of its applications in mathematical finance, engineering and the sciences. Applications in finance include pricing of financial derivatives, such as options on stocks, exotic options and interest rate options. The filtering problem and its solution is presented as an application in engineering. Population models and randomly perturbed equations of physics are given as examples of applications in biology and physics.Only a basic knowledge of calculus and probability is required for reading the book. The text takes the reader from a fairly low technical level to a sophisticated one gradually. Heuristic arguments are often given before precise results are stated, and many ideas are illustrated by worked-out examples. Exercises are provided at the end of chapters to help to test readers' understanding. This book is suitable for advanced undergraduate students, graduate students as well as research workers and practitioners.

This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.