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Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications

BSDEs with Jumps

  • Łukasz Delong

Part of the EAA Series book series (EAAS)

Table of contents

  1. Front Matter
    Pages I-X
  2. Łukasz Delong
    Pages 1-9
  3. Backward Stochastic Differential Equations—The Theory

    1. Front Matter
      Pages 11-11
    2. Łukasz Delong
      Pages 13-35
    3. Łukasz Delong
      Pages 101-111
    4. Łukasz Delong
      Pages 113-122
  4. Backward Stochastic Differential Equations—The Applications

    1. Front Matter
      Pages 123-123
    2. Łukasz Delong
      Pages 125-134
    3. Łukasz Delong
      Pages 173-203
    4. Łukasz Delong
      Pages 235-249
  5. Other Classes of Backward Stochastic Differential Equations

    1. Front Matter
      Pages 251-251
    2. Łukasz Delong
      Pages 253-277
  6. Back Matter
    Pages 279-288

About this book

Introduction

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.

Keywords

BSDEs Brownian Motion Constrained BSDEs Dynamic Risk Measures FBSDEs G-Expectations No-Good-Deal Pricing Perfect Replication Pricing and Hedging of Insurance and Financial Claims Pricing and Hedging under Model Ambiguity Quadratic Pricing and Hedging Random Measures Reflected BSDEs Stochastic Calculus Superhedging Time-Delayed BSDEs Utility Indifference Pricing and Hedging

Authors and affiliations

  • Łukasz Delong
    • 1
  1. 1.Institute of Econometrics, Division of Probabilistic MethodsWarsaw School of EconomicsWarsawPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-5331-3
  • Copyright Information Springer-Verlag London 2013
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-5330-6
  • Online ISBN 978-1-4471-5331-3
  • Series Print ISSN 1869-6929
  • Series Online ISSN 1869-6937
  • Buy this book on publisher's site