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Financial economics without probabilistic prior assumptions

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  • Frank Riedel

Abstract

The treatment of uncertainty in general equilibrium theory in the style of Arrow and Debreu does not require a prior probability on the state space. Finance models nevertheless treat payoffs as random variables, implicitly or explicitly using a known probability distribution. In the light of Knightian uncertainty, we might challenge such an assumption on the probabilistic sophistication of our market model. The present paper shows that one can still develop a sound model of arbitrage pricing under complete Knightian uncertainty as long as certain continuity conditions are met. The pricing functional given by an arbitrage-free market can be identified with a full support martingale measure (instead of equivalent martingale measure). We relate the no-arbitrage theory to economic equilibrium by establishing a variant of the Harrison–Kreps theorem on viability and no arbitrage. Finally, we consider (super) hedging of contingent claims and embed it in a classical infinite-dimensional linear programming problem. Copyright Springer-Verlag Italia 2015

Suggested Citation

  • Frank Riedel, 2015. "Financial economics without probabilistic prior assumptions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(1), pages 75-91, April.
    • Handle: RePEc:spr:decfin:v:38:y:2015:i:1:p:75-91
    DOI: 10.1007/s10203-014-0159-0
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    References listed on IDEAS

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    1. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
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    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets

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