# Fundamental Theorem of Asset Pricing on Measurable Spaces Under Uncertainty

22 Pages Posted: 2 May 2013 Last revised: 12 May 2013

See all articles by Markus Leippold

## Markus Leippold

University of Zurich - Department of Banking and Finance; University of Zurich - Faculty of Economics, Business Administration and Information Technology

## Meriton Ibraimi

University of Zurich - Swiss Banking Institute (ISB)

Date Written: May 11, 2013

### Abstract

It is common in the financial mathematics literature to start by fixing a probability space $(\Omega,\mathcal F,\mathbb P)$, on which the underlying price process is defined. We depart from this route in that we do not fix the prior $\mathbb P$. Under very general assumptions, we recover the Fundamental Theorem of Asset Pricing in discrete time under either a multiple-priors or a prior-free setting. We only require that $(\Omega, \mathcal F)$ is a measurable space, while the multiple priors can be non-equivalent. Furthermore, the initial price of our market model does not need to be constant, but only measurable.

Keywords: Fundamental Theorem of Asset Pricing, uncertainty, multiple priors

JEL Classification: C00, G12

Suggested Citation

Leippold, Markus and Ibraimi, Meriton, Fundamental Theorem of Asset Pricing on Measurable Spaces Under Uncertainty (May 11, 2013). Available at SSRN: https://ssrn.com/abstract=2257882 or http://dx.doi.org/10.2139/ssrn.2257882

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