Price as a Choice Under Nonstochastic Randomness in Finance

16 Pages Posted: 14 Apr 2012

See all articles by Yaroslav Ivanenko

Yaroslav Ivanenko

Banque de France

Bertrand Munier

IAE Sorbonne's Business School, University of Paris1

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Date Written: April 13, 2012

Abstract

Closed sets of finitely-additive probabilities are statistical laws of statistically unstable random phenomena. Decision theory, adapted to such random phenomena, is applied to the problem of valuation of European options. Embedding of the Arrow-Debreu state preference approach to options pricing into decision theoretical framework is achieved by means of considering option prices as decision variables. A version of indifference pricing relation is proposed that extends classical relations for European contingent claims to statistically unstable random behavior of the underlying. A static hedge is proposed that can be called either the model specification hedge or the uncertainty hedge or the generalized Black-Scholes delta. The obtained structure happens to be a convenient way to address such traditional problems of mathematical finance as derivatives valuation in incomplete markets, portfolio choice and market microstructure modeling; and, beyond that, as shown in the appendix, an opportunity to introduce in mathematical finance an alternative interpretation of closed families of finitely-additive probabilities as statistical laws of statistically unstable random phenomena.

Keywords: Statistical instability, Randomness, Finitely-additive measures, Decision theory, Uncertainty profiling, Derivatives Valuation, Portfolio choice, Bid-Ask Spread

Suggested Citation

Ivanenko, Yaroslav and Munier, Bertrand René, Price as a Choice Under Nonstochastic Randomness in Finance (April 13, 2012). NYU Poly Research Paper. Available at SSRN: https://ssrn.com/abstract=2039330 or http://dx.doi.org/10.2139/ssrn.2039330

Yaroslav Ivanenko

Banque de France ( email )

Paris
France

Bertrand René Munier (Contact Author)

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

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

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