A Non Local Free Boundary Problem Arising in a Theory of Financial Bubbles
56 Pages Posted: 4 Nov 2013 Last revised: 13 Nov 2013
Date Written: November 12, 2013
In this paper, we consider an evolution non local free boundary problem that arises in the modeling of speculative bubbles. The solution of the model is the speculative component in the price of an asset. In the framework of viscosity solutions, we show the existence and uniqueness of the solution. We also show the convexity in space of the solution, and various monotonicity properties of the solution and of the free boundary with respect to parameters of the problem.
In order to study the free boundary, we use in particular the fact that the odd part of the solution solves a more standard obstacle problem. We show moreover that the free boundary is Lipschitz continuous, and describe the asymptotics of the free boundary as c, the cost of transacting the asset, goes to zero.
Keywords: Asset-price bubble, finitely lived financial asset, heterogeneous beliefs, obstacle problem, free boundary, non local problem
JEL Classification: C6, G12
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