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Price as a choice under nonstochastic randomness in finance

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  • Y, Ivanenko.
  • B, Munier.

Abstract

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. 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.

Suggested Citation

  • Y, Ivanenko. & B, Munier., 2012. "Price as a choice under nonstochastic randomness in finance," Working papers 381, Banque de France.
    • Handle: RePEc:bfr:banfra:381
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    More about this item

    Keywords

    Statistical instability; Randomness; Finitely-additive measures; Decision theory; Uncertainty profiling; Derivatives Valuation; Portfolio choice; Bid-Ask Spread.;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G02 - Financial Economics - - General - - - Behavioral Finance: Underlying Principles
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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