OPTIMAL CONSUMPTION AND PORTFOLIO IN A BLACK–SCHOLES MARKET DRIVEN BY FRACTIONAL BROWNIAN MOTION

DOI10.1142/S0219025703001432zbMath1180.91266MaRDI QIDQ4467379

Agnès Sulem, Bernt Øksendal, Yaozhong Hu

Publication date: 9 June 2004

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

zbMATH Keywords

fractional Brownian motionsquasi-conditional expectationoptimal consumption and portfoliofractional Black-Scholes marketfractional Itô calculus

Mathematics Subject Classification ID

Gaussian processes (60G15) Stochastic integrals (60H05) Corporate finance (dividends, real options, etc.) (91G50) Portfolio theory (91G10)

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Cites Work

• Unnamed Item
• Unnamed Item
• Itô's formula with respect to fractional Brownian motion and its application
• Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion
• Stochastic analysis of the fractional Brownian motion
• An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions
• Itô-Wiener chaos expansion with exact residual and correlation, variance inequalities
• Arbitrage opportunities for a class of Gladyshev processes
• On a dual pair of spaces of smooth and generalized random variables
• FRACTIONAL WHITE NOISE CALCULUS AND APPLICATIONS TO FINANCE
• On a Generalization of a Stochastic Integral
• Stochastic analysis of fractional brownian motions
• Arbitrage with Fractional Brownian Motion
• On the prediction of fractional Brownian motion
• Stochastic Calculus for Fractional Brownian Motion I. Theory
• Fractional Brownian Motions, Fractional Noises and Applications
• White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance

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