Alexander Melnikov – författare

It is well-known that modern stochastic calculus has been exhaustively developed under usual conditions. Despite such a well-developed theory, there is evidence to suggest that these very convenient technical conditions cannot necessarily be fulfilled in real-world applications.

Optional Processes: Theory and Applications seeks to delve into the existing theory, new developments and applications of optional processes on "unusual" probability spaces. The development of stochastic calculus of optional processes marks the beginning of a new and more general form of stochastic analysis.

This book aims to provide an accessible, comprehensive and up-to-date exposition of optional processes and their numerous properties. Furthermore, the book presents not only current theory of optional processes, but it also contains a spectrum of applications to stochastic differential equations, filtering theory and mathematical finance.

Features

It is well-known that modern stochastic calculus has been exhaustively developed under usual conditions. Despite such a well-developed theory, there is evidence to suggest that these very convenient technical conditions cannot necessarily be fulfilled in real-world applications.

Optional Processes: Theory and Applications seeks to delve into the existing theory, new developments and applications of optional processes on "unusual" probability spaces. The development of stochastic calculus of optional processes marks the beginning of a new and more general form of stochastic analysis.

This book aims to provide an accessible, comprehensive and up-to-date exposition of optional processes and their numerous properties. Furthermore, the book presents not only current theory of optional processes, but it also contains a spectrum of applications to stochastic differential equations, filtering theory and mathematical finance.

Features

Risk Analysis in Finance and Insurance, Third Edition presents an accessible yet comprehensive introduction to the main concepts and methods that transform risk management into a quantitative science. Considering the interdisciplinary nature of risk analysis, the author discusses many important ideas from stochastic analysis, mathematical finance and actuarial science in a simplified manner. He explores the interconnections among these disciplines and encourages readers toward further study of the subject. This edition continues to study risks associated with financial and insurance contracts, using an approach that estimates the value of future payments based on current financial, insurance, and other information.

Features of the third edition

• 12 chapters instead of 8 of the 2nd edition. Two new chapters on Wiener process as a base for financial market modeling. Option pricing in the Bachelier model, the model of Black and Scholes, the Gram-Charlier model. American options and their pricing in the Black-Scholes model

• Several new notions, topics and results that are not reflected yet in other textbooks, and even in monographs (Binomial model with constraints, detailed exposition of quantile hedging technique, Conditional Value at Risk, Range of Value at Risk, applications to equity-linked life insurance)

• Can be regarded as a self-contained issue of courses on Mathematical Finance, Actuarial Science and Risk Management

• Replete with new exercises, problems, hints and solutions

Risk Analysis in Finance and Insurance, Third Edition presents an accessible yet comprehensive introduction to the main concepts and methods that transform risk management into a quantitative science. Considering the interdisciplinary nature of risk analysis, the author discusses many important ideas from stochastic analysis, mathematical finance and actuarial science in a simplified manner. He explores the interconnections among these disciplines and encourages readers toward further study of the subject. This edition continues to study risks associated with financial and insurance contracts, using an approach that estimates the value of future payments based on current financial, insurance, and other information.

Features of the third edition

• 12 chapters instead of 8 of the 2nd edition. Two new chapters on Wiener process as a base for financial market modeling. Option pricing in the Bachelier model, the model of Black and Scholes, the Gram-Charlier model. American options and their pricing in the Black-Scholes model

• Several new notions, topics and results that are not reflected yet in other textbooks, and even in monographs (Binomial model with constraints, detailed exposition of quantile hedging technique, Conditional Value at Risk, Range of Value at Risk, applications to equity-linked life insurance)

• Can be regarded as a self-contained issue of courses on Mathematical Finance, Actuarial Science and Risk Management

• Replete with new exercises, problems, hints and solutions

This book focuses on the application of the partial hedging approach from modern math finance to equity-linked life insurance contracts. It provides an accessible, up-to-date introduction to quantifying financial and insurance risks. The book also explains how to price innovative financial and insurance products from partial hedging perspectives. Each chapter presents the problem, the mathematical formulation, theoretical results, derivation details, numerical illustrations, and references to further reading.

Risk Analysis in Finance and Insurance, Second Edition presents an accessible yet comprehensive introduction to the main concepts and methods that transform risk management into a quantitative science. Taking into account the interdisciplinary nature of risk analysis, the author discusses many important ideas from mathematics, finance, and actuarial science in a simplified manner. He explores the interconnections among these disciplines and encourages readers toward further study of the subject. This edition continues to study risks associated with financial and insurance contracts, using an approach that estimates the value of future payments based on current financial, insurance, and other information.

New to the Second Edition

Reorganized and expanded, this updated book illustrates how to use quantitative methods of stochastic analysis in modern financial mathematics. These methods can be naturally extended and applied in actuarial science, thus leading to unified methods of risk analysis and management.

This book focuses on the application of the partial hedging approach from modern math finance to equity-linked life insurance contracts. It provides an accessible, up-to-date introduction to quantifying financial and insurance risks. The book also explains how to price innovative financial and insurance products from partial hedging perspectives. Each chapter presents the problem, the mathematical formulation, theoretical results, derivation details, numerical illustrations, and references to further reading.

The main subject of the book is stochastic analysis and its various applications to mathematical finance and statistics of random processes. The main purpose of the book is to present, in a short and sufficiently self-contained form, the methods and results of the contemporary theory of stochastic analysis and to show how these methods and results work in mathematical finance and statistics of random processes. The book can be considered as a textbook for both senior undergraduate and graduate courses on this subject. The book can be helpful for undergraduate and graduate students, instructors and specialists on stochastic analysis and its applications.