We introduce and study a class of over-the-counter market models specified by systems of Ordinary Differential Equations (ODE's), in the spirit of Duffie-Gârleanu-Pedersen Duffie et al. (Econometrica 73(1):1815-1847, 2005). The key innovation is allowing for multiple assets. We show the existence and uniqueness of a steady state for these ODE's.
Abstract. We construct a special embedding of the translation quiver ZQ in the three-dimensional affine space R 3 where Q is a finite connected acyclic quiver and ZQ contains a local slice whose quiver is isomorphic to the opposite quiver Q op of Q. Via this embedding, we show that there exists an involutive anti-automorphism of the translation quiver ZQ. As an immediate consequence, we characterize explicitly the group of cluster automorphisms of the cluster algebras of seed (X, Q), where Q and Q op are mutation equivalent.
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