We consider a financial market with liquidity cost as in Çetin, Jarrow and Protter, where the supply function depends on a parameter ε, with ε=0 corresponding to the perfect liquid situation. Using the PDE characterization of Çetin, Soner and Touzi of the super-hedging cost of an option...

We define a coherent risk measures as set-valued maps satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner, Delbaen, Eber and Heath (1998). We then discuss the aggregation issue, i.e. the passage from valued random...

S. Kusuoka [K 01, Theorem 4] gave an interesting dual characterization of law invariant coherent risk measures, satisfying the Fatou property. The latter property was introduced by F. Delbaen [D 02]. In the present note we extend Kusuoka's characterization in two directions, the first one being...

The objective of this paper is to present a model for electricity spot prices and the corresponding forward contracts, which relies on the underlying market of fuels, thus avoiding the electricity non-storability restriction. The structural aspect of our model comes from the fact that the...

We investigate the optimal regulation of energy production reflecting the long-term goals of the Paris Climate Agreement. We analyze the optimal regulatory incentives to foster the development of non-emissive electricity generation when the demand for power is served either by a monopoly or by...