The Black-Scholes model for the pricing of derivative assets, as it has developed during the past twenty five years, uses the expectation of some functional of the underlying asset values (assumed to be representable as a geometric Brownian motion) relative to a martingale measure in the space of geometric-Brownian paths.

The model involves a change of measure, using the Ito calculus, the Girsanov Theorem, and the Radon-Nikodyn Theorem.

By using Henstock's non-absolute integration instead of Lebesgue integration in the domain of geometric-Brownian paths, it is possible to simplify the change of measure argument, reducing it to elementary mathematics.

Whether the Arbitrage Theorem (which justifies the use of the martingale measure in pricing the derivative asset) can be correspondingly simplified, is presented as an unsolved problem.

Dr. Muldowney is a Lecturer in Quantitative Methods, School of International Business, Magee College, University of Ulster, Ireland. He is the Author of "A General Theory of Integration in Function Spaces", Pitman Research Notes in Mathematics, 1988; and Co-author and co-editor of "New Integrals," Springer Lecture Notes in Mathematics, 1990

 
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