Open markets

Ioannis Karatzas and Donghan Kim

Mathematical Finance, 2021, vol. 31, issue 4, 1111-1161

Abstract: An open market is a subset of a larger equity market, composed of a certain fixed number of top‐capitalization stocks. Though the number of stocks in the open market is fixed, their composition changes over time, as each company's rank by market capitalization fluctuates. When one is allowed to invest also in a money market, an open market resembles the entire “closed” equity market in the sense that the market viability (lack of arbitrage) is equivalent to the existence of a numéraire portfolio (which cannot be outperformed). When access to the money market is prohibited, the class of portfolios shrinks significantly in open markets; in such a setting, we discuss the Capital Asset Pricing Model, how to construct functionally generated portfolios, and the concept of universal portfolio.

Date: 2021
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