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

Pierre Bernhard

Chapter Chapter 4 in Numerical Methods in Finance, 2005, pp 91-108 from Springer

Abstract: 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.

Keywords: Transaction Cost; Option Price; Market Model; Differential Game; Interval Model (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-25118-9_4

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DOI: 10.1007/0-387-25118-9_4

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