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A Probabilistic Numerical Method for Fully Non-linear Parabolic Partial Differential Equations

Abstract : The second part of the thesis deals with the optimal production policy under the carbon emission allowance market. The carbon emission allowance market is a market approach to implement Kyoto protocol. We calculated the optimal production in 3 cases: when there is such a market but without any large carbon producer, when there is a large producer who is not market maker, and when there is a large producer market maker. We showed that in second cases, the optimal production is always less than the first case and in the third case it is even less than the second case. On the other hand, we showed that the market maker (if there exist any) can benefit from the market by changing the risk premium of the carbon allowance due to her extra production. The model we used here for the price of carbon allowance is a BSDE. Then we introduce a stochastic optimization problem. The carbon producer wants to maximaze her utility from her wealth. Her wealth consists of two parts: a self--financing portfolio over the carbon emission allowance papers and the benefit from her production. As expected, the optimal production does not depend on the utility. One could pass to a new optimization problem which gives the optimal production. We choose to solve the stochastic optimization problem by the means of HJB equations. We obtained the verification and uniqueness result for the HJB equation. This part is closed by some numerical experiments which shows cases which the large producer can benefit from extra production.
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Contributor : Arash Fahim <>
Submitted on : Saturday, December 11, 2010 - 2:15:27 AM
Last modification on : Wednesday, March 27, 2019 - 4:08:30 PM
Long-term archiving on: : Monday, November 5, 2012 - 1:16:18 PM


  • HAL Id : tel-00540175, version 1



Arash Fahim. A Probabilistic Numerical Method for Fully Non-linear Parabolic Partial Differential Equations. Mathematics [math]. Ecole Polytechnique X, 2010. English. ⟨tel-00540175⟩



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