Optimal Stopping and Free Boundary Problems

Disclosing a fascinating connection between optimal stopping problems in probability and free-boundary problems this comprehensive book covers classic methods of solution and more recent ones. Using minimal tools and key examples the book exposes optimal stopping problems at its basic principles.

A fascinating connection between optimal stopping and free-boundary problems are covered by this book. The analysis uses minimal tools and focuses on key examples. The general theory of optimal stopping is exposed at its basic principles in both discrete and continuous time. It marries the classic methods of solution with more recent ones and a detailed chapter on stochastic processes makes the material more accessible to a wider cross-disciplinary audience. The book is an ideal compendium for an interested reader wishing to master stochastic calculus via fundamental examples. Areas of application where examples are worked out in full detail include financial mathematics, financial engineering, and mathematical statistics. The book will appeal to graduate and postgraduate students, researchers, and practitioners.

A comprehensive treatment of optimal stopping and free-boundary problems ranging from pure theoretical aspects describing methods of solution to specific examples worked out in full detail Marries the three classic problem formulations due to Lagrange (18th century), Mayer (19th century) and Bolza (1913) with the modern problem formulation based on the maximum functional to produce a unifying theory Deals with the principles of smooth and continuous fit in a unifying way Presents complete solutions to option problems (American, Russian, Asian) using local time-space calculus and nonlinear integral equations Presents solutions to problems of optimal prediction of the ultimate maximum opening new avenues for research Includes supplementary material: sn.pub/extras

Klappentext

This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.

Inhalt
Optimal stopping: General facts.- Stochastic processes: A brief review.- Optimal stopping and free-boundary problems.- Methods of solution.- Optimal stopping in stochastic analysis.- Optimal stopping in mathematical statistics.- Optimal stopping in mathematical finance.- Optimal stopping in financial engineering.