TL;DR
This paper investigates the properties of numeraire markets, where the market portfolio maximizes expected logarithmic growth, and provides an example of a stable, asymptotic numeraire market within open markets.
Contribution
It introduces a model of a numeraire market with continuous semimartingale stocks and demonstrates its asymptotic stability, advancing understanding of market dynamics.
Findings
The market portfolio can serve as the numeraire in certain market conditions.
An example of an asymptotically stable numeraire market is constructed.
The model applies to open markets with high capitalization stocks.
Abstract
In a stock market, the numeraire portfolio, if it exists, is the portfolio with the highest expected logarithmic growth rate at all times. A numeraire market is a stock market for which the market portfolio is the numeraire portfolio. We study open markets, markets comprising the higher capitalization stocks within a broad equity universe. The stocks we consider are represented by continuous semimartingales, and we construct an example of a numeraire market that is asymptotically stable.
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Taxonomy
TopicsStochastic processes and financial applications · Economic theories and models