  In this paper, we present a probabilistic numerical algorithm combining
dynamic programming, Monte Carlo simulations and local basis regressions to
solve non-stationary 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 size of the local hypercubes involved in the
regressions, 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.
This model takes into account electricity demand, cointegrated fuel prices,
carbon price and random outages of power plants. It computes the optimal level
of investment in each generation technology, considered as a whole, w.r.t. the
electricity spot price. This electricity price is itself built according to a
new extended structural model. In particular, it is a function of several
factors, among which the installed capacities. The evolution of the optimal
generation mix is illustrated on a realistic numerical problem in dimension
eight, i.e. with two different technologies and six random factors.
