By Łukasz Delong
Backward stochastic differential equations with jumps can be utilized to resolve difficulties in either finance and insurance.
Part I of this booklet provides the speculation of BSDEs with Lipschitz turbines pushed through a Brownian movement and a compensated random degree, with an emphasis on these generated by means of step tactics and Lévy strategies. It discusses key effects and methods (including numerical algorithms) for BSDEs with jumps and stories filtration-consistent nonlinear expectancies and g-expectations. half I additionally specializes in the mathematical instruments and proofs that are the most important for figuring out the theory.
Part II investigates actuarial and monetary purposes of BSDEs with jumps. It considers a common monetary and assurance version and offers with pricing and hedging of assurance equity-linked claims and asset-liability administration difficulties. It also investigates excellent hedging, superhedging, quadratic optimization, software maximization, indifference pricing, ambiguity danger minimization, no-good-deal pricing and dynamic danger measures. half III provides another worthy sessions of BSDEs and their applications.
This booklet will make BSDEs extra obtainable to those that have an interest in making use of those equations to actuarial and monetary difficulties. it will likely be important to scholars and researchers in mathematical finance, threat measures, portfolio optimization in addition to actuarial practitioners.
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