Risk-neutral measure

Engineering

Discrete mathematics

Capital asset pricing model

Statistics

Computer security

Fundamental theorem of asset pricing

Probabilistic logic

Arbitrage

Economics

Duality (order theory)

Computer science

Mathematical optimization

Asset (computer security)

Mechanical engineering

Database

Mathematics

Pointwise

Econometrics

Discrete time and continuous time

Mathematical analysis

Measure (data warehouse)

Mathematical economics

Finance

Cover (algebra)

Probability measure

Arbitrage pricing theory

Mathematics of Operations Research

We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain abstract (pointwise) fundamental theorem of asset pricing and pricing–hedging duality. Our results are general and, in particular, cover both the so-called model independent case as well as the classical probabilistic case of Dalang–Morton–Willinger. Our analysis is scenario-based: a model specification is equivalent to a choice of scenarios to be considered. The choice can vary between all scenarios and the set of scenarios charged by a given probability measure. In this way, our framework interpolates between a model with universally acceptable broad assumptions and a model based on a specific probabilistic view of future asset dynamics.

Pointwise Arbitrage Pricing Theory in Discrete Time