Mathematical Finance (q-fin.MF)

Abstract: We propose two parametric approaches to price swing contracts with firm constraints. Our objective is to create approximations for the optimal control, which represents the amounts of energy purchased throughout the contract. The first approach involves explicitly defining a parametric function to model the optimal control, and the parameters using stochastic gradient descent-based algorithms. The second approach builds on the first one, replacing the parameters with neural networks. Our numerical experiments demonstrate that by using Langevin-based algorithms, both parameterizations provide, in a short computation time, better prices compared to state-of-the-art methods (like the one given by Longstaff and Schwartz).