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 Financial 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
