Ebook: Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications: BSDEs with Jumps
Author: Łukasz Delong (auth.)
- Tags: Quantitative Finance, Actuarial Sciences, Continuous Optimization, Probability Theory and Stochastic Processes
- Series: EAA Series
- Year: 2013
- Publisher: Springer-Verlag London
- Edition: 1
- Language: English
- pdf
Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance.
Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and Lévy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory.
Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications.
This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.
Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance.
Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and L?vy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory.
Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications.
This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.
Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance.
Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and L?vy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory.
Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications.
This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.
Content:
Front Matter....Pages I-X
Front Matter....Pages 11-11
Stochastic Calculus....Pages 13-35
Backward Stochastic Differential Equations—The General Case....Pages 37-78
Forward-Backward Stochastic Differential Equations....Pages 79-99
Numerical Methods for FBSDEs....Pages 101-111
Nonlinear Expectations and g-Expectations....Pages 113-122
Front Matter....Pages 123-123
Combined Financial and Insurance Model....Pages 125-134
Linear BSDEs and Predictable Representations of Insurance Payment Processes....Pages 135-150
Arbitrage-Free Pricing, Perfect Hedging and Superhedging....Pages 151-171
Quadratic Pricing and Hedging....Pages 173-203
Utility Maximization and Indifference Pricing and Hedging....Pages 205-219
Pricing and Hedging Under a Least Favorable Measure....Pages 221-234
Dynamic Risk Measures....Pages 235-249
Front Matter....Pages 251-251
Other Classes of BSDEs....Pages 253-277
Introduction....Pages 1-9
Back Matter....Pages 279-288
Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance.
Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and L?vy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory.
Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications.
This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.
Content:
Front Matter....Pages I-X
Front Matter....Pages 11-11
Stochastic Calculus....Pages 13-35
Backward Stochastic Differential Equations—The General Case....Pages 37-78
Forward-Backward Stochastic Differential Equations....Pages 79-99
Numerical Methods for FBSDEs....Pages 101-111
Nonlinear Expectations and g-Expectations....Pages 113-122
Front Matter....Pages 123-123
Combined Financial and Insurance Model....Pages 125-134
Linear BSDEs and Predictable Representations of Insurance Payment Processes....Pages 135-150
Arbitrage-Free Pricing, Perfect Hedging and Superhedging....Pages 151-171
Quadratic Pricing and Hedging....Pages 173-203
Utility Maximization and Indifference Pricing and Hedging....Pages 205-219
Pricing and Hedging Under a Least Favorable Measure....Pages 221-234
Dynamic Risk Measures....Pages 235-249
Front Matter....Pages 251-251
Other Classes of BSDEs....Pages 253-277
Introduction....Pages 1-9
Back Matter....Pages 279-288
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