Chapter 1 BSDEs Driven by Lévy Processes
1.1 Preliminaries: notations and theorems
1.2 BSDEs for Lévy processes
1.2.1 Comparison theorem
1.2.2 An existence and uniqueness theorem
1.3 BSDEs with reflecting barriers
1.3.1 Introduction and preliminaries
1.3.2 BSDEs with one reflecting barrier: comparison
1.3.3 BSDEs with two reflecting barriers
1.3.4 Comparison theorem
1.4 RBSDEs with time delayed generators
1.4.1 Introduction
1.4.2 Preliminaries and notations
1.4.3 Priori estimates
1.4.4 Existence and uniqueness of the solution
1.5 Lp-solutions for RBSDEs with time delayed generators
1.5.1 Preliminaries and notations
1.5.2 Priori estimates
1.5.3 Existence and uniqueness of the solution
1.6 BSPDES for Lévy processes
1.6.1 Introduction
1.6.2 Preliminaries: notations and lemmas
1.6.3 BSPDEs driven by Lévy processes
1.6.4 Concluding remarks
Chapter 2 Finan Markets Driven by Lévy Processes
2.1 The power utility maximization problem
2.1.1 Introduction
2.1.2 The formulation of the problem
2.1.3 Solution in terms of triplets
2.1.4 A particular case
2.1.5 Appendix
2.2 Optimal investment for an insurer: the martingale approach
2.2.1 Introduction
2.2.2 Problem formulation
2.2.3 CARA Utility
2.3 Cooperative hedging in two explicit model
2.3.1 Introduction
2.3.2 Preliminary and notation
2.3.3 Optimal cooperative hedging of the complete case
2.3.4 Optimal cooperative hedging of a volatility jump model
2.4 Cooperative hedging with a higher interest rate for borrowing
2.4.1 Introduction
2.4.2 The model
2.4.3 The optimal cooperative hedging strategy
2.4.4 Two lemmas about BSDE
2.5 Two-agent Pareto optimal cooperative investment
2.5.1 Introduction
2.5.2 The model
2.5.3 Motivation
2.5.4 Main results
2.5.5 Calculating u(x, T0) explicitly
2.5.6 Concluding remarks
2.6 Cooperative hedging under g-expectation constraint
2.6.1 Introduction
2.6.2 The preliminaries about Neyman-Pearson lemma
2.6.3 The problem formulation
2.6.4 Optimal cooperative hedging of the complete case
Chapter 3 Optimal Control via Malliavin Calculus
3.1 Mean-field stochastic maximum principle
3.1.1 Introduction and preliminaries
3.1.2 A brief review of Malliavin calculus for Lévy processes
3.1.3 The stochastic maximum principle
3.2 Partial information maximum principle via Malliavin calculus
3.2.1 Introduction
3.2.2 The stochastic maximum principle
3.2.3 An application
3.3 Stochastic maximum principle for jump-diffusion mean-field FBSDEs
Chapter 4 Pricing Vulnerable Options
4.1 Variable default boundary under jump-diffusion model
4.1.1 The model
4.1.2 Valuation of European vulnerable options
4.1.3 Three specific examples
4.1.4 Appendix
4.2 Random corporate liabilities
4.2.1 The model
4.2.2 Valuation of European vulnerable options
4.2.3 Specific cases of the pricing formula
4.2.4 Conclusion
4.2.5 Appendix
Bibliography

本书主要讲述与Lévy过程驱动的倒向随机微分方程相关的随机控制和金融问题。主要包括：一类Lévy过程相关的Teugel鞅和独立布朗运动联合驱动的倒向随机微分方程、单反射和双反射障碍的倒向随机微分方程的解和比较定理，倒向随机偏微分方程解的存在专享性定理，反射带时滞的倒向随机微分方程的解，以及解的存在专享性；Lévy过程驱动的金融市场中的幂效用优选化问题