2015/12/08 by Robert Fernholz, Fernholz, Robert
Economics, Econometrics and Finance · #91B28 #91G10 #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1512.02478
openalex publication_date 2015/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Markets composed of stocks with capitalization processes represented by positive continuous semimartingales are studied under the condition that the market excess growth rate is bounded away from zero. The following examples of these markets are given: i) a market with a singular covariance matrix and instantaneous relative arbitrage; ii) a market with a singular covariance matrix and no arbitrage; iii) a market with a nonsingular covariance matrix and no arbitrage; iv) a market with a nonsingular covariance matrix and relative arbitrage over an arbitrary time horizon.