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The Robust Control Approach to Option Pricing and Interval Models: An Overview

In: Numerical Methods in Finance

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  • Pierre Bernhard

Abstract

We give an overview of our work since 2000 on an alternate theory of Option pricing and contingent claim hedging based upon the so-called “interval model” of security prices, which let us develop a consistent theory in discrete and continuous trading within the same model, taking transaction costs into account from the Start. The interval model rules out crises on the stock market. While Samuelson's model does not, so does in practice Black and Scholes' theory in its assumption of instantaneous, continuous trading. Our theory does not make use of any probabilistic knowledge (or rather assumption) on market prices. But we show that Black and Scholes theory does not either.

Suggested Citation

  • Pierre Bernhard, 2005. "The Robust Control Approach to Option Pricing and Interval Models: An Overview," Springer Books, in: Michèle Breton & Hatem Ben-Ameur (ed.), Numerical Methods in Finance, chapter 0, pages 91-108, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-25118-9_4
    DOI: 10.1007/0-387-25118-9_4
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    Cited by:

    1. G. Rigatos & P. Siano, 2018. "Stabilization of Mortgage Price Dynamics Using a Boundary PDE Feedback Control Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 16(1), pages 37-56, March.
    2. Henry Lam & Zhenming Liu, 2014. "From Black-Scholes to Online Learning: Dynamic Hedging under Adversarial Environments," Papers 1406.6084, arXiv.org.
    3. Gerasimos G. Rigatos, 2016. "Boundary Control Of The Black–Scholes Pde For Option Dynamics Stabilization," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 1-29, June.
    4. Naïma El Farouq & Pierre Bernhard, 2015. "Proportional Transaction Costs in the Robust Control Approach to Option Pricing: The Uniqueness Theorem," Post-Print hal-01090616, HAL.

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