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Applied Mathematics & Optimization

, Volume 78, Issue 3, pp 469–491 | Cite as

A Comparison Principle for PDEs Arising in Approximate Hedging Problems: Application to Bermudan Options

  • Géraldine BouveretEmail author
  • Jean-François Chassagneux
Article
  • 220 Downloads

Abstract

In a Markovian framework, we consider the problem of finding the minimal initial value of a controlled process allowing to reach a stochastic target with a given level of expected loss. This question arises typically in approximate hedging problems. The solution to this problem has been characterised by Bouchard et al. (SIAM J Control Optim 48(5):3123–3150, 2009) and is known to solve an Hamilton–Jacobi–Bellman PDE with discontinuous operator. In this paper, we prove a comparison theorem for the corresponding PDE by showing first that it can be rewritten using a continuous operator, in some cases. As an application, we then study the quantile hedging price of Bermudan options in the non-linear case, pursuing the study initiated in Bouchard et al. (J Financial Math 7(1):215–235, 2016).

Keywords

Stochastic target problems Comparison principle Quantile hedging Bermudan options 

Mathematics Subject Classification

Primary 49L25 60J60 93E20 Secondary 49L20 35K55 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Géraldine Bouveret
    • 1
    Email author
  • Jean-François Chassagneux
    • 2
  1. 1.University of OxfordOxfordUK
  2. 2.Laboratoire de Probabilités et Modèles Aléatoires CNRS, UMR 7599Université Paris DiderotParisFrance

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