Stochastic Calculus Under Sublinear Expectation and Volatility Uncertainty

By Christian Bannasch

Research Paper (postgraduate) from the year 2017 in the subject Mathematics - Stochastics, grade: 1,7, LMU Munich, language: English, abstract: Venture into the uncharted territories of probability with a groundbreaking exploration of stochastic calculus under model uncertainty, guided by the pioneering work of Shige Peng. This book unveils the profound implications of sublinear expectations, offering a revolutionary approach to financial modeling, risk management, and stochastic analysis where classical probabilistic assumptions falter. Discover how sublinear expectation spaces provide a robust framework for handling ambiguity and Knightian uncertainty, surpassing the limitations of traditional linear expectations. Delve into the heart of G-Brownian motion, a cornerstone of this theory, and witness its unique characteristics unfold, challenging conventional notions of Brownian motion. Unravel the intricacies of It 's integral in the G-setting, extending its power to a broader class of stochastic processes and paving the way for innovative applications in areas such as derivative pricing and hedging under uncertainty. The book meticulously constructs the mathematical machinery required to navigate this new landscape, from the representation theorem for sublinear expectations to the completion of functional spaces, ensuring a rigorous and accessible treatment of the subject. Explore the concept of capacity related to G-Expectation, essential for understanding the behavior of G-Brownian motion. Witness the extension of It 's integral to stopping times, further enhancing the applicability of the theory. Master the intricacies of It 's formula in the context of G-Brownian motion, a vital tool for solving stochastic differential equations and analyzing complex systems. This book is not merely a theoretical treatise; it is a practical guide for researchers, practitioners, and graduate students seeking to push the boundaries of stochastic analysis and unlock the potential

• Format: Paperback
• Language: English
• ISBN: 3346105253
• ISBN13: 9783346105257
• Release Date: February 2020
• Publisher: Grin Verlag
• Length: 68 Pages
• Weight: 0.22 lbs.
• Dimensions: 0.2" x 5.8" x 8.3"