Stochastic Calculus Under Sublinear Expectation and Volatility Uncertainty
Seiten
2020
|
20001 A. 1. Auflage
GRIN Verlag
978-3-346-10525-7 (ISBN)
GRIN Verlag
978-3-346-10525-7 (ISBN)
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Research Paper (postgraduate) from the year 2017 in the subject Mathematics - Stochastics, grade: 1,7, LMU Munich, language: English, abstract: Detailed results of stochastic calculus under probability model uncertainty have been proven by Shige Peng. At first, we give some basic properties of sublinear expectation E. One can prove that E has a representaion as the Supremum of a specific set of well known linear expectation. P is called uncertainty set and characterizes the probability model uncertainty.
Based on the results of Hu and Peng ([HP09]) we prove that P is a weakly compact set of probability measures. Based on the work of Peng et. Al. we give the definition and properties of maximal distribution and G-normal Distribution. Furthermore, G-Brownian motion and its corresponding G-expectation will be constructed. Briefly speaking, a G -Brownian motion (Bt)t 0 is a continuous process with independent and stationary increments under a given sublinear expectation E.
In this work, we use the results in [LP11] and study Ito's integral of a step process . Ito's integral with respect to G-Brownian motion is constructed for a set of stochastic processes which are not necessarily quasi-continuous. Ito's integral will be defined on an interval [0, ] where is a stopping time. This allows us to define Ito's integral on a larger space. Finally, we give a detailed proof of Ito's formula for stochastic processes.
Based on the results of Hu and Peng ([HP09]) we prove that P is a weakly compact set of probability measures. Based on the work of Peng et. Al. we give the definition and properties of maximal distribution and G-normal Distribution. Furthermore, G-Brownian motion and its corresponding G-expectation will be constructed. Briefly speaking, a G -Brownian motion (Bt)t 0 is a continuous process with independent and stationary increments under a given sublinear expectation E.
In this work, we use the results in [LP11] and study Ito's integral of a step process . Ito's integral with respect to G-Brownian motion is constructed for a set of stochastic processes which are not necessarily quasi-continuous. Ito's integral will be defined on an interval [0, ] where is a stopping time. This allows us to define Ito's integral on a larger space. Finally, we give a detailed proof of Ito's formula for stochastic processes.
| Erscheinungsdatum | 08.02.2020 |
|---|---|
| Sprache | englisch |
| Maße | 148 x 210 mm |
| Gewicht | 112 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Schlagworte | Calculus • Expectation • stochastic • sublinear • Uncertainty • Under • Volatility |
| ISBN-10 | 3-346-10525-3 / 3346105253 |
| ISBN-13 | 978-3-346-10525-7 / 9783346105257 |
| Zustand | Neuware |
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