As the specificities of the model vary greatly depending on the industrial sector, we have decided to focus initially on the case of the electricity producer. This case is particularly interesting for several reasons: the energy and heat production sector accounts for nearly 30% of greenhouse gas emissions in the European Union; secondly, an electricity producer can continuously modify the carbon intensity of its production by substituting two means of production (e.g. by using a gas-fired power station rather than a coal-fired power station which emits more CO2 for the same production), unlike other industrial sectors where the reduction in the carbon intensity of production is achieved through investments in new means of production; Finally, the inelasticity of the demand for electricity and the continuous quotation of the price of electricity make it possible to obtain realistic random models for the electricity price process.
We model the behaviour of an electricity producer with a production fleet consisting of n different means of production (thermal power plants, nuclear power plants, dams, wind turbines, etc.). This producer is subject to the CO2 emission quota system. For a fixed period of compliance with CO2 emissions (typically one year), the producer optimises its production plan, taking into account the uncertain conditions of the market on which it sells its production. He may then be interested in buying/selling CO2 allowances at a higher or lower price, as at the end of the period he must surrender as many permits as CO2 emitted by his installations or pay a penalty (100 euros) per tonne of CO2 not covered.
CarbonQuant evaluates the indifference price of a permit. In financial mathematics, the indifference price of a contract is defined as the smallest value of buying the contract without changing the expected wealth compared to that which would be obtained without buying. In the context of modelling in an uncertain environment, solving the Hamilton-Jacobi-Bellman equations (the stochastic control equations) associated with the situation with the purchase of the contract and without the purchase of the contract provides a means of calculating the indifference price.