Pointwise Arbitrage Pricing Theory in Discrete Time

TL;DR

This paper introduces a versatile, scenario-based framework for pricing and hedging derivatives in discrete-time markets, unifying model-independent and probabilistic approaches with minimal assumptions.

Contribution

It develops a general, pointwise fundamental theorem and duality for asset pricing, bridging model-independent and probabilistic methods in discrete-time markets.

Findings

Unified framework for model-independent and probabilistic pricing

Abstract fundamental theorem of asset pricing established

Scenario-based approach allows flexible model specification

Abstract

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 an abstract (pointwise) Fundamental Theorem of Asset Pricing and Pricing--Hedging Duality. Our results are general and in particular include so-called model independent results of Acciao et al. (2016), Burzoni et al. (2016) as well as seminal results of Dalang et al. (1990) in a classical probabilistic approach. 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.