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Title: Robustness of Quadratic Hedging Strategies in Finance via Backward Stochastic Differential Equations with Jumps

We consider a backward stochastic differential equation with jumps (BSDEJ) which is driven by a Brownian motion and a Poisson random measure. We present two candidate-approximations to this BSDEJ and we prove that the solution of each candidate-approximation converges to the solution of the original BSDEJ in a space which we specify. We use this result to investigate in further detail the consequences of the choice of the model to (partial) hedging in incomplete markets in finance. As an application, we consider models in which the small variations in the price dynamics are modeled with a Poisson random measure with infinite activity and models in which these small variations are modeled with a Brownian motion or are cut off. Using the convergence results on BSDEJs, we show that quadratic hedging strategies are robust towards the approximation of the market prices and we derive an estimation of the model risk.
Authors:
 [1] ;  [2] ;  [3]
  1. University of Oslo, Center of Mathematics for Applications (Norway)
  2. Technische Universität München, Chair of Mathematical Finance (Germany)
  3. Ghent University, Department of Applied Mathematics, Computer Science and Statistics (Belgium)
Publication Date:
OSTI Identifier:
22469711
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 72; Journal Issue: 3; Other Information: Copyright (c) 2015 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BROWNIAN MOVEMENT; CONVERGENCE; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; RANDOMNESS; STOCHASTIC PROCESSES; VARIATIONS