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- Optimal Switching with Applications to Energy Tolling Agreements
Optimal Switching with Applications to Energy Tolling Agreements
- By Rene Carmona
- Published 01/28/2008
- Asset optimization
- Unrated
Rene Carmona
- Director of Graduate Studies of the Bendheim Center for Finance
- Member of the Program in Applied and Computational Mathematics
- Associate Member of the Department of Mathematics
- Elected IMS Fellow in 1984
- Member of AMS, IMS, SIAM,
We consider the problem of optimal switching with finite horizon. This special case of stochastic impulse control naturally arises in the analysis of operational flexibility of exotic energy derivatives. The current practice relies on strips of European spark spread Call options that ignore the operational constraints of the asset. Instead, we propose a new approach based on recursive optimal stopping. Our model directly demonstrates that the optimal dispatch policies can be conveniently described with the aid of ‘switching boundaries’, similar to the free boundaries of standard American options. The thrust of our contribution is a new method of numerical solution based on Monte Carlo regressions. The scheme uses dynamic programming to simultaneously approximate the optimal switching times along all the simulated paths. Convergence analysis is carried out and numerical results are illustrated with a variety of concrete examples. We benchmark and compare our scheme to alternative numerical methods. As an aside, we also contribute to the numerical analysis of reflected backward stochastic differential equations and quasivariational inequalities.
