Equilibrium in a reinsurance market with short sale constraints

This paper deals with the existence of equilibrium in a dynamic reinsurance market with short sale constraints, driven by a marked point process, as studied in Bernis and Jouini (2001). We use the set of reinsurance treaties as consumption set, which is the positive orthant of some Banach lattice that can be identified to a space $H^q$ of martingales, $q\in [1, +\infty[$. The properness of preferences is a key assumption for us to prove the existence of an equilibrium. We provide a sufficient condition for the preferences to be proper in term of loading factor of the reinsurance premium.