Robust Control and CAPMs under a Quadratic Security Market Model

Abstract

This study assumes homothetic robust Epstein-Zin utility and analyzes the consumption-investment problem and CAPMs under a quadratic security market model in which interest rates, the market price of risk, the variances and covariances of asset returns, and inflation rates are stochastic. First, we demonstrate that homothetic robust Epstein-Zin utility is interpreted as homothetic stochastic differential utility. Then, we show that robust investors determine the ''worst-case probability'' and the optimal consumption-investment. We clarify the theoretical structures of robust control. We derive a robust version of the two-factor CAPM and show that the CAPM can contribute to solving both the equity premium puzzle and the risk-free rate puzzle. Furthermore, we derive a testable robust ICAPM and demonstrate that the testable ICAPM is consistent with our quadratic security market model. JEL classification C61, D81, G11, G12