Stochastic Burgers PDEs with random coefficients and a generalization of the Cole-Hopf transformation

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Englezos, Nikolaos¹  Frangos, Nikolaos E.²  Kartala, Xanthi-Isidora²  Yannacopoulos, Athanasios N.² 

[1] Univ Piraeus, Dept Banking & Financial Management, Piraeus 18534, Greece

[2] Athens Univ Econ & Business, Dept Stat, Athens 10434, Greece

关键词: Stochastic Burgers equation;    Random coefficients;    Generalized Cole-Hopf transformation;    Stochastic heat equation;    Stochastic Feynman-Kac formulas;    Controllability;    Contingent claim pricing;   

DOI  :  10.1016/j.spa.2013.03.001

来源: Elsevier

【 摘 要 】

This paper studies forward and backward versions of the random Burgers equation (RBE) with stochastic coefficients. First, the celebrated Cole-Hopf transformation reduces the forward RBE to a forward random heat equation (RHE) that can be treated pathwise. Next we provide a connection between the backward Burgers equation and a system of FBSDEs. Exploiting this connection, we derive a generalization of the Cole-Hopf transformation which links the backward RBE with the backward RHE and investigate the range of its applicability. Stochastic Feynman-Kac representations for the solutions are provided. Explicit solutions are constructed and applications in stochastic control and mathematical finance are discussed. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free