Pointwise Arbitrage Pricing Theory in Discrete Time

2016/12/22 by Burzoni, Matteo, Frittelli, Marco, Hou, Zhaoxu +2 · 1 citation
#FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR)

paper · doi:10.48550/arxiv.1612.07618

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.

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