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A General Maximum Principle for Anticipative Stochastic Control and Applications to Insider Trading

In: Advanced Mathematical Methods for Finance

Author

Listed:
  • Giulia Di Nunno

    (University of Oslo, CMA, Department of Mathematics
    Norwegian School of Economics and Business Administration)

  • Olivier Menoukeu Pamen

    (University of Oslo, CMA, Department of Mathematics
    University of the Witwatersrand, Programme in Advanced Mathematics of Finance, School of Computational and Applied Mathematics)

  • Bernt Øksendal

    (University of Oslo, CMA, Department of Mathematics
    Norwegian School of Economics and Business Administration)

  • Frank Proske

    (University of Oslo, CMA, Department of Mathematics)

Abstract

In this paper we suggest a general stochastic maximum principle for optimal control of anticipating stochastic differential equations driven by a Lévy-type noise. We use techniques of Malliavin calculus and forward integration. We apply our results to study a general optimal portfolio problem of an insider. In particular, we find conditions on the insider information filtration which are sufficient to give the insider an infinite wealth. We also apply the results to find the optimal consumption rate for an insider.

Suggested Citation

  • Giulia Di Nunno & Olivier Menoukeu Pamen & Bernt Øksendal & Frank Proske, 2011. "A General Maximum Principle for Anticipative Stochastic Control and Applications to Insider Trading," Springer Books, in: Giulia Di Nunno & Bernt Øksendal (ed.), Advanced Mathematical Methods for Finance, chapter 0, pages 181-221, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18412-3_7
    DOI: 10.1007/978-3-642-18412-3_7
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