Free access to paper on 'Optimal portfolio under fractional stochastic environment'


  • Author: Statistics Views
  • Date: 17 June 2019

Each week, we select a recently published article and offer either free access or highlight a recent open access publication. This week's is from Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics and is available from the July 2019 issue.

Optimal portfolio under fractional stochastic environment

Jean‐Pierre Fouque and Ruimeng Hu

Mathematical Finance, Volume 29, Issue 3, July 2019, pages 697-734


thumbnail image: Free access to paper on 'Optimal portfolio under fractional stochastic environment'

Rough stochastic volatility models have attracted a lot of attention recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (non‐Markovian) fractional stochastic environment (for all values of the Hurst index H E 0,1). We rigorously establish a first‐order approximation of the optimal value, when the return and volatility of the underlying asset are functions of a stationary slowly varying fractional Ornstein–Uhlenbeck process. We prove that this approximation can be also generated by a fixed zeroth‐ order trading strategy providing an explicit strategy which is asymptotically optimal in all admissible controls. Furthermore, we extend the discussion to general utility functions, and obtain the asymptotic optimality of this fixed strategy in a specific family of admissible strategies.

Related Topics

Related Publications

Related Content

Site Footer


This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.