Erratum to: A Comparison Principle for PDEs Arising in Approximate Hedging Problems: Application to Bermudan Options
| Autor: | Géraldine Bouveret, Jean-François Chassagneux |
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| Rok vydání: | 2017 |
| Předmět: |
Comparison theorem
0209 industrial biotechnology Mathematical optimization Control and Optimization Applied Mathematics Mathematical finance Markov process 02 engineering and technology 01 natural sciences Continuous operator 010104 statistics & probability symbols.namesake 020901 industrial engineering & automation Operator (computer programming) symbols Initial value problem 0101 mathematics Expected loss Mathematics Quantile |
| Zdroj: | Applied Mathematics & Optimization. 78:493-493 |
| ISSN: | 1432-0606 0095-4616 |
| DOI: | 10.1007/s00245-017-9438-9 |
| Popis: | 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). |
| Databáze: | OpenAIRE |
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