Continuous-time capital asset pricing model

This thesis studies the equilibrium behavior of continuous-time capital markets with various market assumptions. These assumptions include different settings of the investment opportunity set and consideration of the variability of the number of shares outstanding of stocks and the investment horizons of investors. Two capital asset pricing models (CAPMs) are established for every case. One of these CAPM focuses on the study of the relationship between the terminal rate of return of any given portfolio and the benchmark portfolios. The other CAPM focuses on the instantaneous rate of return. The market portfolios (and their substitutes for some cases) of all market situations are explicitly derived given homogeneous expectations. The mean-variance efficiencies with a specific terminal time are then investigated. It is proved that some of these market portfolios must be inefficient for a non-zero investment horizon. Moreover, the instantaneous efficiency of portfolios is studied for some market situations. The CAPMs are then developed based on the conditions of each market situation.