NO-ARBITRAGE IN A NUMERAIRE-INDEPENDENT MODELING FRAMEWORK

作者：Herdegen Martin^*

来源：Mathematical Finance, 2017, 27(2): 568-603.

DOI：10.1111/mafi.12088

• numeraire-independent modeling
• no-arbitrage
• maximal strategies
• fundamental theorem of asset pricing
• nonnegative wealth

The classic approach to modeling financial markets consists of four steps. First, one fixes a currency unit. Second, one describes in that unit the evolution of financial assets by a stochastic process. Third, one chooses in that unit a numeraire, usually the price process of a positive asset. Fourth, one divides the original price process by the numeraire and considers the class of admissible strategies for trading. This approach has one fundamental drawback: Almost all concepts, definitions, and results, including no-arbitrage conditions like NA, NFLVR, and NUPBR depend by their very definition, at least formally, on initial choices of a currency unit and a numeraire. In this paper, we develop a new framework for modeling financial markets, which is not based on ex-ante choices of a currency unit and a numeraire. In particular, we introduce a numeraire-independent notion of no-arbitrage and derive its dual characterization. This yields a numeraire-independent version of the fundamental theorem of asset pricing (FTAP). We also explain how the classic approach and other recent approaches to modeling financial markets and studying no-arbitrage can be embedded in our framework.

• 出版日期2017-4