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A stochastic maximum principle for processes driven by fractional Brownian motion

Author

Listed:
  • Biagini, Francesca
  • Hu, Yaozhong
  • Øksendal, Bernt
  • Sulem, Agnès

Abstract

We prove a stochastic maximum principle for controlled processes X(t)=X(u)(t) of the formdX(t)=b(t,X(t),u(t)) dt+[sigma](t,X(t),u(t)) dB(H)(t),where B(H)(t) is m-dimensional fractional Brownian motion with Hurst parameter . As an application we solve a problem about minimal variance hedging in an incomplete market driven by fractional Brownian motion.

Suggested Citation

  • Biagini, Francesca & Hu, Yaozhong & Øksendal, Bernt & Sulem, Agnès, 0. "A stochastic maximum principle for processes driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 233-253, July.
    • Handle: RePEc:eee:spapps:v:100:y::i:1-2:p:233-253
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    Citations

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    Cited by:

    1. Tomas Björk & Henrik Hult, 2005. "A note on Wick products and the fractional Black-Scholes model," Finance and Stochastics, Springer, vol. 9(2), pages 197-209, April.
    2. Bender, Christian, 2014. "Backward SDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2892-2916.
    3. Zhang, H.Y. & Bai, L.H. & Zhou, A.M., 2009. "Insurance control for classical risk model with fractional Brownian motion perturbation," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 473-480, February.
    4. Yu, Xianye, 2019. "Non-Lipschitz anticipated backward stochastic differential equations driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.

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