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On Option-Valuation in Illiquid Markets: Invariant Solutions to a Nonlinear Model

In: Mathematical Control Theory and Finance

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  • Ljudmila A. Bordag

    (Halmstad University)

Abstract

Summary The present model describes a perfect hedging strategy for a large trader. In this case the hedging strategy affects the price of the underlying security. The feedback-effect leads to a nonlinear version of the Black-Scholes partial differential equation. Using Lie group theory we reduce in special cases the partial differential equation to some ordinary differential equations. The Lie group found for the model equation gives rise to invariant solutions. Families of exact invariant solutions for special values of parameters are described.

Suggested Citation

  • Ljudmila A. Bordag, 2008. "On Option-Valuation in Illiquid Markets: Invariant Solutions to a Nonlinear Model," Springer Books, in: Andrey Sarychev & Albert Shiryaev & Manuel Guerra & Maria do Rosário Grossinho (ed.), Mathematical Control Theory and Finance, pages 71-94, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69532-5_5
    DOI: 10.1007/978-3-540-69532-5_5
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