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

作者：Berestycki Henri^*; Monneau Regis; Scheinkman Jose A

来源：Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 2014, 372(2028): 20130404.

DOI：10.1098/rsta.2013.0404

• obstacle problem
• free boundary
• non-local problem
• asset-price bubble
• finitely lived financial asset
• heterogeneous beliefs

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 C-infinity and describe the asymptotics of the free boundary as c, the cost of transacting the asset, goes to zero.

• 出版日期2014-11-13
• 单位中国医学科学院北京协和医院