容量限制理论和相关应用非线性数学期望

Chapter 1 Limit theory about capacity

1.1 Law of large numbers for capacity

1.1.1 Ambiguity urn models

1.1.2 Law of large numbers for Bernoulli trials with ambiguity

1.1.3 General urn models

1.2 Weighted central limit theorem under sublinear expectations

1.2.1 Notations and preliminaries

1.2.2 Main result and proof

1.3 Berry—Esseen theory under linear expectation

1.4 Central limit theorem for capacity

Chapter 2 Discrete martingale under sublinear expectation

2.1 Definitions

2.2 SL—martingale and related inequalities

Chapter 3 Multi—dimensional G—Brownian motion

3.1 Kunita—Watanabe inequalities for multi—dimensional G—Brownian motion

3.1.1 Preliminaries

3.1.2 Mutual variation process and Kunita—Watanabe inequalities for multi—dimensional G—Brownian motion

3.2 Tanaka formula for multi—dimensional G—Brownian motion

Chapter 4 Stability problem for stochastic differential equations driven by G—Browman motion

4.1 Stability theorem for stochastic differential equations driven by G—Brownian motion

4.1.1 Stability theorem for G—SDE under integral—Lipschitz condition

4.1.2 Stability about backward stochastic differential equations driven by G—Brownian motion

4.1.3 Existence and uniqueness for forward—backward stochastic differential equations driven by G—Brownian motion

4.1.4 Stability about forward—backward stochastic differential equations driven by G—Brownian motion

4.2 Exponential stability for stochastic differential equations driven by G—Brownian motion

4.2.1 Asymptotic Exponential stability for stochastic differential equations driven by G—Brownian motion

Optimal control problems under G—expectation

4.3.1 Forward and backward stochastic differential equations driven by G—Brownian motion

4.3.2 Optimal control problems under G—expectation

Chapter 5 Applications about G—Brownian motion in optimal consumption and portfolio

5.1 Preliminaries

5.2 Optimal consumption and portfolio Rules under volatility uncertainty

5.3 Mutual fund theorem under volatility uncertainty

5.4 A special case

Chapter 6 Functional solution about stochastic differential equation driven by G—Brownian motion

6.1 Introduction

6.2 Functional solution about stochastic differential equation driven by G—Brownian motion

6.3 Some classical models

6.3.1 Autonomous case

6.3.2 One—factor Hull—White model

6.3.3 Homogeneous linear G—stochastic differential equations

6.4 Conclusion

Bibliography

Symbol Index

《容量限制理论和相关应用非线性数学期望（英文版）》内容分为六章。它们分别是：Chapter 1 Limit theory about capacity、Chapter 2 Discrete martingale under sublinear expectation、Chapter 3 Multi—dimensional G—Brownian motion、Chapter 4 Stability problem for stochastic differential equations driven by G—Browman motion、Chapter 5 Applications about G—Brownian motion in optimal consumption and portfolio、Chapter 6 Functional solution about stochastic differential equation driven by G—Brownian motion、Bibliography Symbol、Index。