A Probabilistic Numerical Method for Optimal Multiple Switching Problems in High Dimension

Abstract

In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations, and local basis regressions to solve nonstationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize the problem, of the regression basis used to approximate conditional expectations, and of the truncating time horizon. To make the method viable for problems in high dimension and long time horizon, we extend a memory reduction method to the general Euler scheme, so that, when performing the numerical resolution, the storage of the Monte Carlo simulation paths is not needed. Then, we apply this algorithm to a model of optimal investment in power plants in dimension eight, i.e., with two different technologies and six random factors.

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