Xavier Warin has been working for 30 years at EDF, one of the leading electricity operator in Europe. After working 8 years in the simulation of Nuclear Reactors, he began to work in finance at the opening of the energy market in Europe at the end of the nineties. He is now an expert in stochastic optimization methods. His main contributions have been the development of numerical methods used for general asset valorization, specially for the valorization of some complex derivatives on the energy Markets. He is now involved in the development of algorithms based on machine learning to solve problems in high dimension. At EDF, he has achieved many studies on risk and he is the founder of an open source library : the Stochastic Optimization Library (StOpt).
In this paper, the author uses the mean–variance hedging criterion to value contracts in incomplete markets.
In this paper algorithms are developed using the Hamilton–Jacobi–Bellman approach for parabolic partial integrodifferential equations related to the quadratic hedging strategy in incomplete markets.