joint work with Raul Tempone, Sören Wolfers
We consider the pricing American basket options in a multivariate setting, including the Heston and the rough Bergomi models. In high dimensions, nonlinear PDEs methods for solving the problem become prohibitively costly due to the curse of dimensionality. Our novel method uses Monte Carlo simulation and the optimization of exercise strategies parametrized as randomized exercise strategies. Integrating analytically over the random exercise decision yields an objective function that is differentiable with respect to perturbations of the exercise rate, even for finitely many sampled paths.
joint work with Saif Benjaafar, Daniel Jiang, Xiang Li
We consider a product rental network with a fixed number of rental units distributed across multiple locations. Because of the randomness in demand and in the length of the rental periods and in unit returns, there is a need to periodically reposition inventory. We formulate the problem as a Markov Decision Process and offer a characterization of the optimal policy. In addition, we propose a new cutting-plane-based approximate dynamic programming algorithm that leverages the structural properties. A novel convergence analysis, together with promising numerical experiments, is provided.