Price as a Choice Under Nonstochastic Randomness in Finance

34 Pages Posted: 15 May 2012 Last revised: 20 Jan 2015

See all articles by Yaroslav Ivanenko

Yaroslav Ivanenko

Banque de France

Bertrand Munier

IAE Sorbonne's Business School, University of Paris1

Multiple version iconThere are 2 versions of this paper

Date Written: May 1, 2012


Arrow-Debreu state preference approach to derivatives pricing is embedded into decision theoretical framework. Derivatives prices are considered as decision variables. Axiomatic decision theory, concerned with the attitude toward uncertainty and existence of closed in *-weak topology sets of finitely-additive probabilities is applied. A version of indifference pricing relation is obtained that extends classical relations for European contingent claims. A formal expression of a static hedge is proposed that can be called either the model specification hedge or the uncertainty hedge. The obtained structure happens to be a convenient way of addressing such traditional problems of mathematical finance as derivatives valuation in incomplete markets, portfolio choice and market microstructure modeling. An alternative interpretation of the closed sets of finitely-additive probabilities as statistical laws of statistically unstable (nonstochastic) random phenomena is discussed.

Keywords: statistical instability, randomness, finitely-additive measures, decision theory, uncertainty profiling, derivatives valuation, portfolio choice, bid-ask spread

JEL Classification: C18, C44, D81, G02, G11, G13

Suggested Citation

Ivanenko, Yaroslav and Munier, Bertrand René, Price as a Choice Under Nonstochastic Randomness in Finance (May 1, 2012). Banque de France Working Paper No. 381, Available at SSRN: or

Yaroslav Ivanenko (Contact Author)

Banque de France ( email )


Bertrand René Munier

IAE Sorbonne's Business School, University of Paris1 ( email )

8bis, rue de la Croix-Jarry
Paris, Ile de France 75013
+330607016861 (Phone)


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