A non-local free boundary problem arising in a theory of financial bubbles | Zendy

Henri Berestycki | Zendy; Régis Monneau | Zendy; José Scheinkman | Zendy

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A non-local free boundary problem arising in a theory of financial bubbles

Author(s) -

Henri Berestycki,

Régis Monneau,

José Scheinkman

Publication year - 2014

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2013.0404

Subject(s) - free boundary problem , uniqueness , boundary (topology) , obstacle problem , monotonic function , mathematics , boundary value problem , regular polygon , space (punctuation) , asset (computer security) , obstacle , mathematical economics , mathematical analysis , computer science , law , geometry , operating system , computer security , political science

We consider an evolution non-local free boundary problem that arises in the modelling 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 that the solution is convex in space, and establish several monotonicity properties of the solution and of the free boundary with respect to parameters of the problem. 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 that the free boundary is [Formula: see text] and describe the asymptotics of the free boundary as c, the cost of transacting the asset, goes to zero.

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