Francois Delarue: Singular FBSDEs and Carbon Emissions Market

I will present a simple model for pricing emission allowances on carbon markets. A special care will paid to the analysis of the stochastic differential equations deriving from the modeling.

First, I will explain how to model the equilibrium regime of a cap-and-trade carbon market as a singular forward-backward system of stochastic differential equations. The word ``singular'' here refers to the specific structure of the equations modeling the market: the forward equation is degenerate and the backward equation is driven by a Heaviside boundary condition. I will explain the need to relax the notion of solution to a backward equation to make the underlying modeling well-posed. I will also discuss the specific influence of the cap condition and explain that the underlying forward process develops a Dirac mass at maturity time.

I will also discuss the law of the forward process just before maturity time. Specifically, I will investigate the existence of a density for the transition kernel of the forward process.

Joint works with R. Carmona, N. Touzi and G.E. Espinosa.