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Optimal switching with applications to energy tolling agreements.

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We consider the problem of optimal switching with finite horizon. This special case of stochastic impulse control naturally arises during analysis of operational flexibility of exotic energy derivatives. The current practice for such problems relies on Markov decision processes that have poor dimension-scaling properties, or on strips of spark spread options that ignore the operational constraints of the asset.; To overcome both of these limitations, we propose a new framework based on recursive optimal stopping. Our model demonstrates that the optimal dispatch policies can be described with the aid of 'switching boundaries', similar to standard American options. In turn, this provides new insight regarding the qualitative properties of the value function.; Our main 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 then benchmark and compare our scheme to alternative numerical methods. On a mathematical level, we contribute to the numerical analysis of reflected backward stochastic differential equations and quasi-variational inequalities. The final part of the dissertation proposes fruitful extensions to tackle other financial problems such as gas storage, exhaustible resources, hedging supply guarantees and energy risk management.
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