Nonlinear Expectations and Stochastic Calculus under Uncertainty: with Robust CLT and G-Brownian Motion
sep. 2019 · Probability Theory and Stochastic Modelling Bog 95 · Springer Nature
E-bog
212
Sider
reportBedømmelser og anmeldelser verificeres ikke Få flere oplysninger
Om denne e-bog
This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author.
This book is based on Shige Peng’s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes.
This book is based on Shige Peng’s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes.
With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter.
Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful.
Om forfatteren
Shige Peng received his PhD in 1985 at Université Paris-Dauphine, in the direction of mathematics and informatics, and 1986 at University of Provence, in the direction of applied mathematics. He now is a full professor in Shandong University. His main research interests are stochastic optimal controls, backward SDEs and the corresponding PDEs, stochastic HJB equations. He has received the Natural Science Prize of China (1995), Su Buqing Prize of Applied Mathematics (2006), TAN Kah Kee Science Award (2008), Loo-Keng Hua Mathematics Award (2011), and the Qiu Shi Award for Outstanding Scientists (2016).
Bedøm denne e-bog
Fortæl os, hvad du mener.
Oplysninger om læsning
Smartphones og tablets
Installer appen Google Play Bøger til Android og iPad/iPhone. Den synkroniserer automatisk med din konto og giver dig mulighed for at læse online eller offline, uanset hvor du er.
Bærbare og stationære computere
Du kan høre lydbøger, du har købt i Google Play via browseren på din computer.
e-læsere og andre enheder
Hvis du vil læse på e-ink-enheder som f.eks. Kobo-e-læsere, skal du downloade en fil og overføre den til din enhed. Følg den detaljerede vejledning i Hjælp for at overføre filerne til understøttede e-læsere.
