A stochastic maximum principle for processes driven by fractional Brownian motion.
type: Item
instance of: scholarly article
title: A stochastic maximum principle for processes driven by fractional Brownian motion.
zbMATH Open document ID: 1064.93048
DOI: 10.1016/S0304-4149(02)00105-9
author: Francesca Biagini
author: Yaozhong Hu
author: B. Øksendal
author: Agnès Sulem
published in: Stochastic Processes and their Applications
publication date: 2005-02-25T00:00:00Z
review text: A stochastic maximum principle for a controlled process \(X(t)\) governed by the stochastic differential equation of the form \[ \text{d}X(t)=b(t,X(t),u(t))\,\text{d}t +\sigma (t,X(t),u(t))\,\text{d}B^H(t) \] is proved where \(B^H(t)\) is an \(m\)-dimensional fractional Brownian motion with the Hurst parameter \(H\in (1/2,1)^m\), \(b:[0,T]\times R^n\times U\to R^n\) and \(\sigma : [0,T]\times R^n\times U\to R^{n\times n}\) are given \(C^1\) functions and the control process \(u:[0,T]\times \Omega \to U\subset R^k\) is adapted. The stochastic fractional backward equation for the adjoint process is discussed in the linear case. As an application a problem of minimal variance hedging in an incomplete market driven by fractional Brownian motion is solved.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 2138926
zbMATH Keywords: stochastic maximum principle
zbMATH Keywords: stochastic control
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2138926