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Titlebook: Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications; BSDEs with Jumps Łukasz Delong Textbo

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期刊全称Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications
期刊简称BSDEs with Jumps
影响因子2023Łukasz Delong
视频video
发行地址Contains the most recent advances in BSDEs.Applies BSDEs with jumps to insurance and finance.Full notation and results are given, followed by applications
学科分类EAA Series
图书封面Titlebook: Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications; BSDEs with Jumps Łukasz Delong Textbo
影响因子.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
Pindex Textbook 2013
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Quadratic Pricing and Hedging First, we deal with a minimal hedging error in a mean-square sense. The hedging error is evaluated both under an equivalent martingale measure and the real-world measure. Next, we investigate locally risk minimizing strategies which lead to non-self-financing investment portfolio processes. Finally
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Utility Maximization and Indifference Pricing and Hedgingthe investment strategy under which the expected exponential utility of the insurer’s terminal wealth is maximized. We characterize the optimal value function of the optimization problem and the optimal investment strategy by a nonlinear BSDE. Next, we solve the exponential indifference pricing and
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Pricing and Hedging Under a Least Favorable Measurericing and hedging under model ambiguity. We find the hedging strategy which minimizes the expected terminal shortfall under a least favorable probability measure specifying the probability model for the risk factors and we set the price which offsets this worst shortfall. Next, we deal with no-good
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Other Classes of BSDEsDE in which the terminal condition and the generator depend on the past values of the solution. Next, we consider a reflected BSDE in which the solution is constrained to stay above a barrier. Finally, we deal with a constrained BSDE in which all components of the solution are forced to satisfy a co
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