On a stochastic heat equation with first order fractional noises and applications to finance

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:396

Article

Jiang, Yiming^1,2  Wang, Xingchun^1,2  Wang, Yongjin^1,2,3 

[1] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[2] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

[3] Nankai Univ, Sch Business, Tianjin 300071, Peoples R China

关键词: First order noise;    Adjoint operator;    Existence and uniqueness;    Regularity;    Term structure;    Arbitrary-free;   

DOI  :  10.1016/j.jmaa.2012.07.003

来源: Elsevier

【 摘 要 】

In this paper, we propose a class of stochastic heat equations with first order fractional noises. We define a first order noise through the adjoint operator of the first order operator, where the operation of the stochastic integral can be avoided. In this framework, the existence and uniqueness of the solution of the equation will be established. Further, we give the regularity of the solution. Finally, we model the term structure of forward rate with the solutions and give the conditions under which the market is arbitrary-free. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free