Free boundary problem of Barenblatt equation in stochastic control

Xiaoshan  Chen; Fahuai  Yi

doi:10.3934/dcdsb.2016003

Article Contents

2016, Volume 21, Issue 5: 1421-1434. Doi: 10.3934/dcdsb.2016003

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Free boundary problem of Barenblatt equation in stochastic control

Xiaoshan Chen^1, and
Fahuai Yi^2,

1.
School of Mathematical Sciences, South China Normal University, Guangzhou 510631
2.
School of Finance, Guangdong University of Foreign Studies, Guangzhou 510006

Received: January 2014

Revised: March 2014

Published: July 2016

Abstract / Introduction Related Papers Cited by

Abstract

The following type of parabolic Barenblatt equations
min {$\partial_t V - \mathcal{L}_1 V, \partial_t V-\mathcal{L}_2 V$} = 0
is studied, where $\mathcal{L}_1$ and $\mathcal{L}_2$ are different elliptic operators of second order. The (unknown) free boundary of the problem is a divisional curve, which is the optimal insured boundary in our stochastic control problem. It will be proved that the free boundary is a differentiable curve.
To the best of our knowledge, this is the first result on free boundary for Barenblatt Equation. We will establish the model and verification theorem by the use of stochastic analysis. The existence of classical solution to the HJB equation and the differentiability of free boundary are obtained by PDE techniques.

Keywords:

Mathematics Subject Classification: 35R35, 60G40, 91B70, 93E20.

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