Dual dominance: how Harry Markowitz and William Ziemba impacted portfolio management

Models for determining a portfolio of investment decisions in risky assets have been at the forefront of financial research for almost a century. Among the celebrated researchers are Harry Markowitz and William Ziemba. These titans devoted their working years to developing quantitative models and adapting the models to changes in financial markets and investor attitudes. This paper presents a general lens through which the Markowitz mean-variance model and the Ziemba capital growth model can be viewed. This lens is risk-sensitive stochastic control. The optimal control approach places the expected utility, mean-variance, and capital growth models in a common setting to elucidate their connection. In particular, benchmarking and risk factors, two standard refinements to control risk, are seamlessly incorporated into the stochastic control model. The solution to the risk-sensitive control problem isolates the effect of benchmarks and factors to provide insights into model-based portfolios.