Financial economics without probabilistic prior assumptions

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 Knighti...

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Bibliographic Details
Published in:Decisions in economics and finance Vol. 38; no. 1; pp. 75 - 91
Main Author: Riedel, Frank
Format: Journal Article
Language:English
Published: Milan Springer Milan 01.04.2015
Springer Nature B.V
Subjects:
Arbitrage
Asset backed securities
Black swan event
Econometrics
Economic theory
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Equilibrium
Finance
Financial economics
Free markets
Hedging
Linear algebra
Linear programming
Management
Market equilibrium
Mathematical analysis
Operations Research/Decision Theory
Prices
Probability
Probability distribution
Public Finance
Random variables
Sophistication
Studies
Uncertainty
Volatility
D53
Infinite-dimensional linear programming
Full support martingale measure
Probability-free finance
G12
Fundamental theorem of asset pricing
Superhedging
ISSN:1593-8883, 1129-6569
Online Access:Get full text
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Summary: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.
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ISSN:1593-8883
1129-6569
DOI:10.1007/s10203-014-0159-0