Acta Applicandae Mathematica

, Volume 2, Issue 2, pp 139–158

On the theory of option pricing

  • A. Bensoussan

DOI: 10.1007/BF00046576

Cite this article as:
Bensoussan, A. Acta Appl Math (1984) 2: 139. doi:10.1007/BF00046576


The objective of this article is to provide an axiomatic framework in order to define the concept of value function for risky operations for which there is no market. There is a market for assets, whose prices are characterized as stochastic processes. The method consists of constructing a portfolio of these assets which will mimic the risks involved in the operation. We follow the terminology of the theory of options although the set-up goes beyond that particular problem.

AMS (MOS) subject classifications (1980)

00A69 60G 90A 

Key words

Stochastic control optimal stopping option pricing hedging portfolio complete markets contingent claim European and American claims 

Copyright information

© D. Reidel Publishing Company 1984

Authors and Affiliations

  • A. Bensoussan
    • 1
  1. 1.University of Paris-Dauphine and INRIALe ChesnayFrance