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).
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03 July 2017
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This research has been sponsored by the Natixis Foundation for Quantitative Finance.
This work has been written during the author’s PhD at Imperial College London, Department of Mathematics.
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Bouveret, G., Chassagneux, JF. A Comparison Principle for PDEs Arising in Approximate Hedging Problems: Application to Bermudan Options. Appl Math Optim 78, 469–491 (2018). https://doi.org/10.1007/s00245-017-9413-5
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DOI: https://doi.org/10.1007/s00245-017-9413-5